60.1.495 problem 498

Internal problem ID [10509]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 498
Date solved : Monday, January 27, 2025 at 08:31:39 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.391 (sec). Leaf size: 99

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

\begin{align*} y &= 1 \\ y &= \frac {\sin \left (\operatorname {RootOf}\left (8 \sqrt {3}\, c_{1} \textit {\_Z} -8 \sqrt {3}\, x \textit {\_Z} +\cos \left (\textit {\_Z} \right )^{2}-48 c_{1}^{2}+96 c_{1} x -48 x^{2}-\textit {\_Z}^{2}\right )\right )}{6}+\frac {5}{6} \\ y &= \frac {\sin \left (\operatorname {RootOf}\left (8 \sqrt {3}\, c_{1} \textit {\_Z} -8 \sqrt {3}\, x \textit {\_Z} -\cos \left (\textit {\_Z} \right )^{2}+48 c_{1}^{2}-96 c_{1} x +48 x^{2}+\textit {\_Z}^{2}\right )\right )}{6}+\frac {5}{6} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.375 (sec). Leaf size: 160

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

\begin{align*} y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {1-\text {$\#$1}} \text {arcsinh}\left (\sqrt {3} \sqrt {\text {$\#$1}-1}\right )}{\sqrt {3} \sqrt {\text {$\#$1}-1}}-\sqrt {3 (\text {$\#$1}-1)+1} \sqrt {1-\text {$\#$1}}\&\right ][-2 x+c_1] \\ y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {1-\text {$\#$1}} \text {arcsinh}\left (\sqrt {3} \sqrt {\text {$\#$1}-1}\right )}{\sqrt {3} \sqrt {\text {$\#$1}-1}}-\sqrt {3 (\text {$\#$1}-1)+1} \sqrt {1-\text {$\#$1}}\&\right ][2 x+c_1] \\ y(x)\to 1 \\ \end{align*}