Internal problem ID [11297]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VIII, Linear differential equations of the second order. Article 54. Change of
independent variable. Page 127
Problem number: Ex 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+y \,{\mathrm e}^{2 x}={\mathrm e}^{4 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
dsolve(diff(y(x),x$2)+(2*exp(x)-1)*diff(y(x),x)+exp(2*x)*y(x)=exp(4*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\frac {x}{2}-{\mathrm e}^{x}} \sinh \left (\frac {x}{2}\right ) c_{2} +{\mathrm e}^{\frac {x}{2}-{\mathrm e}^{x}} \cosh \left (\frac {x}{2}\right ) c_{1} +{\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}+6 \]
✓ Solution by Mathematica
Time used: 0.121 (sec). Leaf size: 39
DSolve[y''[x]+(2*Exp[x]-1)*y'[x]+Exp[2*x]*y[x]==Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -4 e^x+e^{2 x}+c_1 e^{-e^x}+c_2 e^{x-e^x}+6 \]