Thank you for reporting, we will resolve it shortly
Q.
The value of the constant ' $m$ ' and ' $c$ ' for which $y=m x+c$ is a solution of the differential equation $D^2 y-3 D y-4 y=-4 x$.
Differential Equations
Solution:
$y=m x+c ; \frac{d y}{d x}=m ; \frac{d^2 y}{d x^2}=0$
substituting in $\frac{ d ^2 y }{ dx ^2}-3 \frac{ dy }{ dx }-4 y =-4 x$
$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
$m=+1 \text { and } c=-3 / 4 \Rightarrow(B)$