60.1.462 problem 465

Internal problem ID [10476]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 465
Date solved : Monday, January 27, 2025 at 07:54:45 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y {y^{\prime }}^{2}+2 x y^{\prime }-9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.183 (sec). Leaf size: 92

dsolve(y(x)*diff(y(x),x)^2+2*x*diff(y(x),x)-9*y(x) = 0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= \operatorname {RootOf}\left (-\ln \left (x \right )-\int _{}^{\textit {\_Z}}\frac {\textit {\_a}^{2}+\sqrt {9 \textit {\_a}^{2}+1}+1}{\textit {\_a} \left (\textit {\_a}^{2}-7\right )}d \textit {\_a} +c_{1} \right ) x \\ y &= \operatorname {RootOf}\left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}-\frac {\textit {\_a}^{2}-\sqrt {9 \textit {\_a}^{2}+1}+1}{\textit {\_a} \left (\textit {\_a}^{2}-7\right )}d \textit {\_a} +c_{1} \right ) x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.128 (sec). Leaf size: 112

DSolve[-9*y[x] + 2*x*D[y[x],x] + y[x]*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} \text {Solve}\left [\int \frac {y(x)}{x \left (\frac {y(x)^2}{x^2}-\sqrt {\frac {9 y(x)^2}{x^2}+1}+1\right )}d\frac {y(x)}{x}&=-\log (x)+c_1,y(x)\right ] \\ \text {Solve}\left [\int \frac {y(x)}{x \left (\frac {y(x)^2}{x^2}+\sqrt {\frac {9 y(x)^2}{x^2}+1}+1\right )}d\frac {y(x)}{x}&=-\log (x)+c_1,y(x)\right ] \\ y(x)\to 0 \\ \end{align*}