Internal problem ID [5442]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary
problems. Page 132
Problem number: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 51
dsolve(y(x)*diff(y(x),x$3)+3*diff(y(x),x)*diff(y(x),x$2)-2*y(x)*diff(y(x),x$2)-2*diff(y(x),x)^2+y(x)*diff(y(x),x)=exp(2*x),y(x), singsol=all)
\begin{align*} y = \sqrt {-2 c_{3} {\mathrm e}^{x} x +{\mathrm e}^{2 x}+2 c_{2} {\mathrm e}^{x}-2 c_{1}} y = -\sqrt {-2 c_{3} {\mathrm e}^{x} x +{\mathrm e}^{2 x}+2 c_{2} {\mathrm e}^{x}-2 c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.387 (sec). Leaf size: 65
DSolve[y[x]*y'''[x]+3*y'[x]*y''[x]-2*y[x]*y''[x]-2*y'[x]^2+y[x]*y'[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {e^{2 x}+e^x (c_3 x+2 c_2)+2 c_1} y(x)\to \sqrt {e^{2 x}+e^x (c_3 x+2 c_2)+2 c_1} \end{align*}