The value of the constant ' m ' and ' c ' for which y=m x+c is a solution of the differential equation D2 y-3 D y-4 y=-4 x.

Question

The value of the constant ' m ' and ' c ' for which y=m x+c is a solution of the differential equation D2 y-3 D y-4 y=-4 x. (A) is m =-1; c =3 / 4 (B) is m =1; c =-3 / 4 (C) no such real m , c (D) is m =1 ; c =3 / 4

Tardigrade Admin · Accepted Answer

y=m x+c ; (d y/d x)=m ; (d2 y/d x2)=0 substituting in ( d 2 y / dx 2)-3 ( dy / dx )-4 y =-4 x 0-3 m-4(m x+c)=-4 x -3 m-4 c-4 m x=-4 x -(3 m+4 c)=4 x(m-1) (1) is true for all real x if m=+1 text and c=-3 / 4 ⇒(B)

Q. The value of the constant ' $m$ ' and ' $c$ ' for which $y = m x + c$ is a solution of the differential equation $D^{2} y - 3 Dy - 4 y = - 4 x$ .

is $m = - 1$ ; $c = 3/4$

is $m = 1$ ; $c = - 3/4$

no such real $m, c$

is $m = 1; c = 3/4$

Q. The value of the constant ' m ' and ' c ' for which y=mx+c is a solution of the differential equation D2y−3Dy−4y=−4x.

is m=−1; c=3/4

is m=1; c=−3/4

no such real m,c

is m=1;c=3/4

y=mx+c;dxdy​=m;dx2d2y​=0 substituting in dx2d2y​−3dxdy​−4y=−4x 0−3m−4(mx+c)=−4x −3m−4c−4mx=−4x −(3m+4c)=4x(m−1) (1) is true for all real x if m=+1 and c=−3/4⇒(B)

Q. The value of the constant ' $m$ ' and ' $c$ ' for which $y = m x + c$ is a solution of the differential equation $D^{2} y - 3 Dy - 4 y = - 4 x$ .

is $m = - 1$ ; $c = 3/4$

is $m = 1$ ; $c = - 3/4$

no such real $m, c$

is $m = 1; c = 3/4$