Internal problem ID [12202]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 152.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 a y^{\prime }+y a^{2}={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-2*a*diff(y(x),x)+a^2*y(x)=exp(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{a x}+x \,{\mathrm e}^{a x} c_{1} +\frac {{\mathrm e}^{x}}{\left (a -1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.224 (sec). Leaf size: 28
DSolve[y''[x]-2*a*y'[x]+a^2*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x}{(a-1)^2}+e^{a x} (c_2 x+c_1) \]