1.12 problem Problem 11.14

Internal problem ID [4666]

Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section: Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page 95
Problem number: Problem 11.14.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_linear, class A]]

Solve \begin {gather*} \boxed {y^{\prime }-5 y-x^{2} {\mathrm e}^{x}+x \,{\mathrm e}^{5 x}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 38

dsolve(diff(y(x),x)-5*y(x)=x^2*exp(x)-x*exp(5*x),y(x), singsol=all)
 

\[ y \relax (x ) = \left (-\frac {x^{2}}{2}-\frac {x^{2} {\mathrm e}^{-4 x}}{4}-\frac {{\mathrm e}^{-4 x} x}{8}-\frac {{\mathrm e}^{-4 x}}{32}+c_{1}\right ) {\mathrm e}^{5 x} \]

Solution by Mathematica

Time used: 0.228 (sec). Leaf size: 39

DSolve[y'[x]-5*y[x]==x^2*Exp[x]-x*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{32} e^x \left (8 x^2+4 x+1\right )+e^{5 x} \left (-\frac {x^2}{2}+c_1\right ) \\ \end{align*}