Internal problem ID [11105]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.3-1. Equations with
exponential functions
Problem number: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-\left (a +2 \,{\mathrm e}^{a x} b \right ) y^{\prime }+b^{2} {\mathrm e}^{2 a x} y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)-(a+2*b*exp(a*x))*diff(y(x),x)+b^2*exp(2*a*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {a^{2} x +2 \,{\mathrm e}^{a x} b}{2 a}} \left (c_{1} \sinh \left (\frac {a x}{2}\right )+c_{2} \cosh \left (\frac {a x}{2}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 35
DSolve[y''[x]-(a+2*b*Exp[a*x])*y'[x]+b^2*Exp[2*a*x]*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{\frac {b e^{a x}}{a}} \left (b c_2 e^{a x}+a c_1\right )}{a} \]