Internal problem ID [8078]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 498.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (3 y-2\right ) \left (y^{\prime }\right )^{2}-4+4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (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 \relax (x ) = 1 \\ y \relax (x ) = \frac {\sin \left (\RootOf \left (-8 \sqrt {3}\, c_{1} \textit {\_Z} +8 \sqrt {3}\, x \textit {\_Z} -\left (\cos ^{2}\left (\textit {\_Z} \right )\right )+48 c_{1}^{2}-96 x c_{1}+48 x^{2}+\textit {\_Z}^{2}\right )\right )}{6}+\frac {5}{6} \\ y \relax (x ) = \frac {\sin \left (\RootOf \left (8 \sqrt {3}\, c_{1} \textit {\_Z} -8 \sqrt {3}\, x \textit {\_Z} -\left (\cos ^{2}\left (\textit {\_Z} \right )\right )+48 c_{1}^{2}-96 x c_{1}+48 x^{2}+\textit {\_Z}^{2}\right )\right )}{6}+\frac {5}{6} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.461 (sec). Leaf size: 142
DSolve[-4 + 4*y[x] + (-2 + 3*y[x])*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {2 \text {ArcTan}\left (\frac {\sqrt {3 \text {$\#$1}-2}}{\sqrt {3-3 \text {$\#$1}}-1}\right )}{\sqrt {3}}-\sqrt {1-\text {$\#$1}} \sqrt {3 \text {$\#$1}-2}\&\right ][-2 x+c_1] \\ y(x)\to \text {InverseFunction}\left [\frac {2 \text {ArcTan}\left (\frac {\sqrt {3 \text {$\#$1}-2}}{\sqrt {3-3 \text {$\#$1}}-1}\right )}{\sqrt {3}}-\sqrt {1-\text {$\#$1}} \sqrt {3 \text {$\#$1}-2}\&\right ][2 x+c_1] \\ y(x)\to 1 \\ \end{align*}