60.1.398 problem 400

Internal problem ID [10412]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 400
Date solved : Monday, January 27, 2025 at 07:40:41 PM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 77

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

\begin{align*} y &= \frac {x^{3}}{6} \\ y &= \frac {\sqrt {6}\, \sqrt {-c_{1} x}\, x}{3}+c_{1} \\ y &= -\frac {\sqrt {6}\, \sqrt {-c_{1} x}\, x}{3}+c_{1} \\ y &= -\frac {\sqrt {6}\, \sqrt {-c_{1} x}\, x}{3}+c_{1} \\ y &= \frac {\sqrt {6}\, \sqrt {-c_{1} x}\, x}{3}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.616 (sec). Leaf size: 146

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

\begin{align*} \text {Solve}\left [\frac {1}{3} \log (y(x))-\frac {2 \sqrt {x^4-6 x y(x)} \text {arctanh}\left (\frac {x^{3/2}}{\sqrt {x^3-6 y(x)}}\right )}{3 \sqrt {x} \sqrt {x^3-6 y(x)}}&=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {2 \sqrt {x^4-6 x y(x)} \text {arctanh}\left (\frac {x^{3/2}}{\sqrt {x^3-6 y(x)}}\right )}{3 \sqrt {x} \sqrt {x^3-6 y(x)}}+\frac {1}{3} \log (y(x))&=c_1,y(x)\right ] \\ y(x)\to \frac {x^3}{6} \\ \end{align*}