Differential Equations

Differential Equations One Mark Questions PREPARED BY: R.RAJENDRAN. M.A., M. Sc., M. Ed., K.C.SANKARALINGA NADAR HR. SEC. SCHOOL, CHENNAI-21

Choose the Correct Answer • The integrating factor of is (a) log x (b) x2 (c) ex (d) x • If cos x is an integrating factor of the differential equation then P is(a) – cot x (b) cot x(c) tan x (d) – tan x

Choose the Correct Answer • The integrating factor of dx + x dy = e– y sec2y dy is (a) ex (b) e–x (c) ey (d) e–y • The integrating factor of is(a) ex (b) log x(c) 1/x (d) e–x

Choose the Correct Answer • The solution of where m < 0 is (a) x = cemy (b) x = ce–m y(c) x = my + c (d) x = c • y = cx – c2 is the general solution of the differential equation(a) (y’)2 – xy’ + y = 0 (b) y’’ = 0(c) y’ = c (d) (y’)2 + xy’ + y = 0

Choose the Correct Answer • The differential equation of is (a) of order 2 and degree 1 (b) of order 1 and degree 2(c) of order 1 and degree 6 (d) of order 1 and degree 3 • The differential equation of all non-vertical lines in a plane is(a) (b)(c) (d)

Choose the Correct Answer • The differential equation of all circles with center at the origin is(a) xdy + ydx = 0 (b) xdy – ydx = 0 (c) xdx + ydy = 0 (d) xdx – ydy = 0 • The integrating factor of the differential equation is(a) P dx (b) Q dx(c) e Q dx (d) e P dx

Choose the Correct Answer • The complementary function of (D2 + 1)y = e 2x is is(a) (Ax + B)ex (b) A cosx + B sinx (c) (Ax + B)e2x (d) (Ax + B)e– x • The particular integral of (D2 – 4D + 4) y = e2x is(a)(x2/2)e2x (b) xe2x(c) xe– 2x (d) (x/2)e– 2x

Choose the Correct Answer • The differential equation of the family of lines y = mx is(a) (b) ydx – xdy = 0 (c) (d) ydx + xdy = 0 • The degree of the differential equation (a) 1 (b) 2(c) 3 (d) 6

Choose the Correct Answer • The degree of the differential equation where c is a constant(a) 1 (b) 3 (c) – 2 (d) 2 • The differential equation satisfied by all the straight lines in xy plane is(a) = a constant (b) (c) (d)

Choose the Correct Answer • The amount present in a radio active element disintegrates at a rate proportional to its amount. The differential equation corresponding to the above statement is (k is negative)(a) (b) (c) (d) • If then(a) 2xy + y2 – x2 = c (b) x2 + y2 – x + y = c(c) x2 + y2 – 2xy = c (d) x2 – y2 – 2xy = c

Choose the Correct Answer • If y = kex then its differential equation is(a) (b) (c) (d) • The differential equation formed by eliminating a and b from y = ae3x + be–3x is (a) (b) (c) (d)

Choose the Correct Answer • If f’(x) = x and f(1) = 2 then f(x) is(a) (b) (c) (d) • The differential equation formed by eliminating A and B from y = ex (A cosx + B sinx) is (a) y2 + y1 = 0 (b) y2 – y1 = 0(c) y2 – 2y1 + 2y = 0 (d) y2 – 2y1 – 2y = 0

Choose the Correct Answer • On putting y = vx, the homogeneous differential equation x2dy + y(x + y)dx = 0 becomes(a) x dv + (2v + v2)dx = 0 (b) v dx + (2x + x2)dv = 0 (c) v2dx – (x + x2)dv = 0 (d) v dx + (2x + x2)dx = 0 • The integrating factor of the differential equation (a) secx (b) cosx(c) etanx (d) cotx

Choose the Correct Answer • The PI of (3D2 + D – 14)y = 13 e2x is(a) 26xe2x (b) 13xe2x(c) xe2x (d) (x2/2)e2x • The PI of the differential equation f(D)y = eax where f(D) = (D – a) g(D), g(a)  0 is(a) meax (b) (c) g(a)eax (d)

Choose the Correct Answer • The order and degree of the differential equation is(a) 1, 8 (b) 3, 1 (c) 3, 8 (d) 3, 2 • The solution of is(a) y = c ecosx (b) y = c e– sinx(c) y = c e– cosx (d) y = c esinx

Choose the Correct Answer • The PI of (D2 + 1)y = 5 is(a) 5 (b) 5/y (c) x/5 (d) – 5 • The integrating factor of the differential equation (a) log(logy) (b) (c) logy (d) 1/y

Choose the Correct Answer • The particular integral of (D2 – 3D + 2)y = ex is(a) xex (b) – xex(c) ex (d) – ex • The solution of the differential equation xdy + ydx is(a) x2 y2 = c2 (b) y = cx2(c) y = x2 + c (d) xy = c

Choose the Correct Answer • The integrating factor of (a) – log sinx (b) – sinx (c) log sinx (d) cosecx • The order and degree of (a) 1, 2 (b) 2, 1(c) 2, 2 (d) 1, 1

Choose the Correct Answer • The integrating factor of (a) sin2x (b) 1/log x (c) 1/x (d) log x • The order and degree of (a) 1, 4 (b) 2, 3(c) 2, 4 (d) 1, 4

Choose the Correct Answer • The order and degree of the differential equation y’’ = (y – y’3) 2/3 are(a) 2, 3 (b) 3, 3 (c) 3, 2 (d) 2, 2 • The order and degree of the differential equation y’ + (y’’)2 = (x + y’’) 2 are(a) 1, 1 (b) 1, 2 (c) 2, 1 (d) 2, 2

Choose the Correct Answer • The order and degree of the differential equation y’ + (y’’)2 = x(x + y’’) 2 are(a) 2, 2 (b) 2, 1 (c) 1, 2 (d) 1, 1 • The order and degree of the differential equation sin x (dx + dy) = cos x (dx - dy) are(a) 1, 1 (b) 0, 0 (c) 1, 2 (d) 2, 1

Choose the Correct Answer • The differential equation corresponding to y = ax2 + bx + c where a, b, c are arbitrary constants, is (a) y’’’ + y’’ = 0 (b) y’’ = 2a (c) y’’’ = 0 (d) y’’’ – y’’ = 0 • In finding the differential equation corresponding to y = emx where m is the arbitrary constant, then m is (a) y / y’ (b) y’ / y (c) y’ (d) y

Choose the Correct Answer • The order and degree of the differential equation y’ + y2 = x are(a) 2, 1 (b) 1, 1 (c) 1, 0 (d) 0, 1 • The order and degree of the differential equation y’’ + 3y’2 + y3 = 0 are(a) 2, 2 (b) 2, 1 (c) 1, 2 (d) 3, 1

Choose the Correct Answer • The solution of a linear differential equation where P and Q are functions of y is (a) y(I.F) = (b) x(I.F) = (c) y(I.F) = (d) x(I.F) =

Choose the Correct Answer • The solution of a linear differential equation where P and Q are functions of x is (a) y(I.F) = (b) x(I.F) = (c) y(I.F) = (d) x(I.F) =

Choose the Correct Answer • Identify the incorrect statement(a) The order of a differential equation is the order of the highest order derivative occurring in it(b) The degree of the differential equation is the degree of the highest order derivative which occurs in it (the derivatives are free from radicals and fractions)(c) is the first order first degree homogeneous differential equation (d) is a linear differential equation in x

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Differential Equations