82.18.20 problem Ex. 22

Internal problem ID [18842]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Examples on chapter III. page 38
Problem number : Ex. 22
Date solved : Tuesday, January 28, 2025 at 12:26:43 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} {y^{\prime }}^{3}+m {y^{\prime }}^{2}&=a \left (y+m x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 124

dsolve(diff(y(x),x)^3+m*diff(y(x),x)^2=a*(y(x)+m*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{3 \operatorname {RootOf}\left (2 \textit {\_Z} \,m^{2}+3 \,{\mathrm e}^{2 \textit {\_Z}}-8 m \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} a -2 a x +5 m^{2}\right )}-2 \,{\mathrm e}^{2 \operatorname {RootOf}\left (2 \textit {\_Z} \,m^{2}+3 \,{\mathrm e}^{2 \textit {\_Z}}-8 m \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} a -2 a x +5 m^{2}\right )} m +{\mathrm e}^{\operatorname {RootOf}\left (2 \textit {\_Z} \,m^{2}+3 \,{\mathrm e}^{2 \textit {\_Z}}-8 m \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} a -2 a x +5 m^{2}\right )} m^{2}-a m x}{a} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],x]^3+m*D[y[x],x]^2==a*(y[x]+m*x),y[x],x,IncludeSingularSolutions -> True]
 

Timed out