Internal problem ID [5152]
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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+3 y=x^{2}-1} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = {\mathrm e}^{x} \sin \left (\sqrt {2}\, x \right ) c_{2} +{\mathrm e}^{x} \cos \left (\sqrt {2}\, x \right ) c_{1} +\frac {x^{2}}{3}+\frac {4 x}{9}-\frac {7}{27} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 48
DSolve[y''[x]-2*y'[x]+3*y[x]==x^2-1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{27} \left (9 x^2+12 x-7\right )+c_2 e^x \cos \left (\sqrt {2} x\right )+c_1 e^x \sin \left (\sqrt {2} x\right ) \]