40.14.14 problem 35

Internal problem ID [6785]
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
Date solved : Tuesday, January 28, 2025 at 03:10:34 PM
CAS classification : [[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]

\begin{align*} y y^{\prime \prime \prime }+3 y^{\prime } y^{\prime \prime }-2 y y^{\prime \prime }-2 {y^{\prime }}^{2}+y^{\prime } y&={\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (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 \,{\mathrm e}^{x} c_2 -2 c_1} \\ y &= -\sqrt {{\mathrm e}^{2 x}+\left (-2 c_3 x +2 c_2 \right ) {\mathrm e}^{x}-2 c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.341 (sec). Leaf size: 65

DSolve[y[x]*D[y[x],{x,3}]+3*D[y[x],x]*D[y[x],{x,2}]-2*y[x]*D[y[x],{x,2}]-2*D[y[x],x]^2+y[x]*D[y[x],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*}