60.7.158 problem 1749 (book 6.158)

Internal problem ID [11747]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1749 (book 6.158)
Date solved : Monday, January 27, 2025 at 11:33:31 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime } y-3 {y^{\prime }}^{2}+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.104 (sec). Leaf size: 67

dsolve(4*diff(diff(y(x),x),x)*y(x)-3*diff(y(x),x)^2+4*y(x)=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ -\frac {4 \sqrt {y^{{3}/{2}} c_{1} +4 y}}{\sqrt {y}\, c_{1}}-x -c_{2} &= 0 \\ \frac {4 \sqrt {y^{{3}/{2}} c_{1} +4 y}}{\sqrt {y}\, c_{1}}-x -c_{2} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.343 (sec). Leaf size: 43

DSolve[4*y[x] - 3*D[y[x],x]^2 + 4*y[x]*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (c_1{}^2 x^2+2 c_2 c_1{}^2 x-64+c_2{}^2 c_1{}^2\right ){}^2}{256 c_1{}^2} \]