Q 10 please 29345687Which of the following is a second-order linear nonhomogenous ODE?C) sin(x) (y)² + y = 0 D) sin(x)y"y+C) y = ²³ x² + D) y = ²x².A) sin(x)y" + y = 0B) sin(x)y" +y + 3 = 023A) y=e*² +e B) y=e¹² C)y=e³² +e_D) y=e¹By using a suitable substitution, the non-separable ODE xy' = x³ + y, is reduces to a separable ODE of the form:A)u' = = = =1B) u'=xC) xu'+2u=0D) u'= -xFind the general solution of y"-3y'=0A) y =q₁x+c₂e³C) y = ₁+c₂e³xD) y=q₁ +c₂e³xFind the value(s) fork in which the general solution of 3y"+y+ky=0 is of the form c,e¹ + ₂x²,{c₁, c₂, are real constants}A) k = 12B) k=0C) k = 1D) k = /2112.Find an ODE whose basis of the general solution the functions y, = sin 3x, y₂ = cos 3xA)y"-9y=0B) y"+9y=0C) y"-3y=0D) y"+3y=010 The integrating factor of the non-exact D.E. (ex+y+yey) dx + (xey-1) dy = 0(a) e-y4Find the general solution of y'++y = 4x ?B) y=x² +xFind the values for the constants a, b in which the ODE (axy-by²) dx-(x² + 4xy) dy=0 is exact?A) a=3,b=-2B) a=-3,b=-2C) a=3,b=4D) a=0,b=-2By using a suitable substitution, the Bernoulli ODE y'+ xy = y, becomes a linear ODE of the form:A) u'-4xu = -4B) u'-3x = -3uC) u'+3xu = 3D) u'-3xu = -3Find the exact solution for x'y'-y=0, y(1)=1A) y = x² +C-2xB) y=ce²+c₂e²(b)-y11 the general solution for the second order ODE y" + 11y' + 24y = 0(c) y ³a) y = C₁ ex+C₂ e³x(b) y = C₁ ex+C₂ e ³x-8x12 the integrating factor for the first order ODE y' = 3 + 2y is(a) e²(b) e2(c) e 2x(d) e²x(d) y-³(c) y = C₁ e³x +C₂ e³x (d) y = C₁ e

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Q 10 please 29345687Which of the following is a second-order linear nonhomogenous ODE?C) sin(x) (y)² + y = 0 D) sin(x)y&#34;y+C) y = ²³ x² + D) y = ²x².A) sin(x)y&#34; + y = 0B) sin(x)y&#34; +y + 3 = 023A) y=e*² +e B) y=e¹² C)y=e³² +e_D) y=e¹By using a suitable substitution, the non-separable ODE xy' = x³ + y, is reduces to a separable ODE of the form:A)u' = = = =1B) u'=xC) xu'+2u=0D) u'= -xFind the general solution of y&#34;-3y'=0A) y =q₁x+c₂e³C) y = ₁+c₂e³xD) y=q₁ +c₂e³xFind the value(s) fork in which the general solution of 3y&#34;+y+ky=0 is of the form c,e¹ + ₂x²,{c₁, c₂, are real constants}A) k = 12B) k=0C) k = 1D) k = /2112.Find an ODE whose basis of the general solution the functions y, = sin 3x, y₂ = cos 3xA)y&#34;-9y=0B) y&#34;+9y=0C) y&#34;-3y=0D) y&#34;+3y=010 The integrating factor of the non-exact D.E. (ex+y+yey) dx + (xey-1) dy = 0(a) e-y4Find the general solution of y'++y = 4x ?B) y=x² +xFind the values for the constants a, b in which the ODE (axy-by²) dx-(x² + 4xy) dy=0 is exact?A) a=3,b=-2B) a=-3,b=-2C) a=3,b=4D) a=0,b=-2By using a suitable substitution, the Bernoulli ODE y'+ xy = y, becomes a linear ODE of the form:A) u'-4xu = -4B) u'-3x = -3uC) u'+3xu = 3D) u'-3xu = -3Find the exact solution for x'y'-y=0, y(1)=1A) y = x² +C-2xB) y=ce²+c₂e²(b)-y11 the general solution for the second order ODE y&#34; + 11y' + 24y = 0(c) y ³a) y = C₁ ex+C₂ e³x(b) y = C₁ ex+C₂ e ³x-8x12 the integrating factor for the first order ODE y' = 3 + 2y is(a) e²(b) e2(c) e 2x(d) e²x(d) y-³(c) y = C₁ e³x +C₂ e³x (d) y = C₁ e

Accepted Answer

Answered: Image /qna-images/answer/4eb24780-3a77-4861-aed8-e03d41ddbcca.jpg

-3y=0 D) y+3y=0 10 The integrating factor of the non-exact D.E. (ex+y + yey) dx + (xey-1) dy = 0 (a) e-y (b)-y (c) y³ 11 the general solution for the second order ODF " + 11² 1 -3 (d) y-³