Internal problem ID [4629]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 25. Second order differential equations. Test Excercise 25. page 1093
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y-10 \,{\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-4*y(x)=10*exp(3*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{-2 x}+2 \,{\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 28
DSolve[y''[x]-4*y[x]==10*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (e^{4 x} \left (2 e^x+c_1\right )+c_2\right ) \\ \end{align*}