15.19.9 problem 9

Internal problem ID [3293]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 9
Date solved : Monday, January 27, 2025 at 07:31:31 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}+\left (x +y-2 y x \right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 28

dsolve(diff(y(x),x)^3+(x+y(x)-2*x*y(x))*diff(y(x),x)^2-2*diff(y(x),x)*x*y(x)*(x+y(x))=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= {\mathrm e}^{x^{2}} c_{1} \\ y \left (x \right ) &= 1+{\mathrm e}^{-x} c_{1} -x \\ y \left (x \right ) &= c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 36

DSolve[D[y[x],x]^3+(x+y[x]-2*x*y[x])*D[y[x],x]^2-2*D[y[x],x]*x*y[x]*(x+y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \\ y(x)\to c_1 e^{x^2} \\ y(x)\to -x+c_1 e^{-x}+1 \\ \end{align*}