engineering recuitment NIELIT Scientific Assistant Mock Test 2025 Engineering Mathematics Differential Equations Higher Order Linear Differential Equations with Constant Coefficients
If roots of the auxiliary equation of \(\dfrac{d^2y}{dx^2}\;+\;a\dfrac{dy}{dx}\;+\;by=0\) are real and equal, the general solution of the differential equation is
1
\(y=c_1{e^{-\frac{ax}{2}}}\;+\;c_2{e^{\frac{ax}{2}}}\)
2
\(y=(c_1\;+\;c_2x){e^{-\frac{ax}{2}}}\)
3
\( y=(c_1+c_2\ln x){e^{-\frac{ax}{2}}}\)
4
\(y=(c_1\cos \ x +c_2\sin \ x){e^{-\frac{ax}{2}}}\)