Internal problem ID [5174]
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`]]
\[ \boxed {y^{\prime }-5 y=x^{2} {\mathrm e}^{x}-{\mathrm e}^{5 x} x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(diff(y(x),x)-5*y(x)=x^2*exp(x)-x*exp(5*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (x^{2}-2 c_{1} \right ) {\mathrm e}^{x} {\mathrm e}^{4 x}}{2}+\frac {\left (-8 x^{2}-4 x -1\right ) {\mathrm e}^{x}}{32} \]
✓ Solution by Mathematica
Time used: 0.209 (sec). Leaf size: 39
DSolve[y'[x]-5*y[x]==x^2*Exp[x]-x*Exp[5*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{32} e^x \left (8 x^2+4 x+1\right )+e^{5 x} \left (-\frac {x^2}{2}+c_1\right ) \]