Q 2 please 1234567Which of the following is a second-order linear nonhomogenous ODE?A) sin(x)y" + y = 0 B) sin(x)y"+y+3=0 C) sin(x) (y)² + y = 0 D) sin(x)4Find the general solution of y'+-y=4x ? A) y=x² + B) y=x²+0) y = x² + D).Find the values for the constants a, b in which the ODE (axy-by²) dx-(x² + 4xy) dy=0 is exact?XA) 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=-4 B) u'-3x=-3uC) u'+3xu=3D) u'- 3xu = -3Find the exact solution for x'y'-y=0, y(1)=1A) y=e² +e B) y=e¹-² C)y=e=²+e_D)y=e¹By using a suitable substitution, the non-separable ODE xy'=x+y, is reduces to a separable ODE of the1A)u'=-B) u'=xC) xu'+2u=0 D) u'=-xFind the general solution of y"-3y'=0A) y=q₁x+c₂₁e¹C)y=+₂e³xB) y=ce ¹ +ce²D) y=c₁ +₂ede value(s) fork in which the general solution of 3y"+y+ky=0 is of the form ce +exe^c₂,2 are real constants}A) k = 12B) k=0C) k = 1D) k = =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=010 The integrating factor of the non-exact D.E. (ex+y+ye) dx + (xey-1) dy = 0D) y"+3y=0(a) e-(b)-y(c) y ³11 the general solution for the second order ODE y" + 11y' + 24y = 0-8x3xa) y = C₁ ex+C₂ e³x-8x-3x(b) y = C₁ e +C₂ e (c) y = C₁ e +C₂ e³¹ (d) y =12 the integrating factor for the first order ODE y' = 3+2y is(a) e²(b) e²e-2x(d) e²x(c) e(d)

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Q 2 please 1234567Which of the following is a second-order linear nonhomogenous ODE?A) sin(x)y&#34; + y = 0 B) sin(x)y&#34;+y+3=0 C) sin(x) (y)² + y = 0 D) sin(x)4Find the general solution of y'+-y=4x ? A) y=x² + B) y=x²+0) y = x² + D).Find the values for the constants a, b in which the ODE (axy-by²) dx-(x² + 4xy) dy=0 is exact?XA) 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=-4 B) u'-3x=-3uC) u'+3xu=3D) u'- 3xu = -3Find the exact solution for x'y'-y=0, y(1)=1A) y=e² +e B) y=e¹-² C)y=e=²+e_D)y=e¹By using a suitable substitution, the non-separable ODE xy'=x+y, is reduces to a separable ODE of the1A)u'=-B) u'=xC) xu'+2u=0 D) u'=-xFind the general solution of y&#34;-3y'=0A) y=q₁x+c₂₁e¹C)y=+₂e³xB) y=ce ¹ +ce²D) y=c₁ +₂ede value(s) fork in which the general solution of 3y&#34;+y+ky=0 is of the form ce +exe^c₂,2 are real constants}A) k = 12B) k=0C) k = 1D) k = =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=010 The integrating factor of the non-exact D.E. (ex+y+ye) dx + (xey-1) dy = 0D) y&#34;+3y=0(a) e->(b)-y(c) y ³11 the general solution for the second order ODE y&#34; + 11y' + 24y = 0-8x3xa) y = C₁ ex+C₂ e³x-8x-3x(b) y = C₁ e +C₂ e (c) y = C₁ e +C₂ e³¹ (d) y =12 the integrating factor for the first order ODE y' = 3+2y is(a) e²(b) e²e-2x(d) e²x(c) e(d)

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2 + y = u B) sin(x)y+iy' +3=0 C)sin(x)(y') + y = 0 D) sin(x) Find the general solution of y'+ 12y=4x? A)y=x2+/2B)y=x+12cy=2x+12