Internal problem ID [4644]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 25. Second order differential equations. Further problems 25. page 1094
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+3 y-x^{2}+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+3*y(x)=x^2-1,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x} \sin \left (x \sqrt {2}\right ) c_{2}+{\mathrm e}^{x} \cos \left (x \sqrt {2}\right ) c_{1}+\frac {x^{2}}{3}+\frac {4 x}{9}-\frac {7}{27} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 46
DSolve[y''[x]-2*y'[x]+3*y[x]==x^2-1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} x (3 x+4)+e^x \left (c_2 \cos \left (\sqrt {2} x\right )+c_1 \sin \left (\sqrt {2} x\right )\right )-\frac {7}{27} \\ \end{align*}