1.29 problem 30

Internal problem ID [7073]

Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 30.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [[_homogeneous, `class C`], _rational, _dAlembert]

\[ \boxed {y-x {y^{\prime }}^{2}-{y^{\prime }}^{2}=0} \]

Solution by Maple

Time used: 0.078 (sec). Leaf size: 53

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

\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (x +1+\sqrt {\left (x +1\right ) \left (c_{1} +1\right )}\right )^{2}}{x +1} \\ y \left (x \right ) &= \frac {\left (-x -1+\sqrt {\left (x +1\right ) \left (c_{1} +1\right )}\right )^{2}}{x +1} \\ \end{align*}

Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 57

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

\begin{align*} y(x)\to x-c_1 \sqrt {x+1}+1+\frac {c_1{}^2}{4} \\ y(x)\to x+c_1 \sqrt {x+1}+1+\frac {c_1{}^2}{4} \\ y(x)\to 0 \\ \end{align*}