Internal problem ID [8076]
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]
\[ \boxed {\left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y=0} \]
✓ Solution by Maple
Time used: 0.141 (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 \left (x \right ) = 1 \\ y \left (x \right ) = \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 x c_{1} -48 x^{2}-\textit {\_Z}^{2}\right )\right )}{6}+\frac {5}{6} \\ y \left (x \right ) = \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 x c_{1} +48 x^{2}+\textit {\_Z}^{2}\right )\right )}{6}+\frac {5}{6} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.379 (sec). Leaf size: 132
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 {\arctan \left (\frac {\sqrt {3 \text {$\#$1}-2}}{\sqrt {3-3 \text {$\#$1}}}\right )}{\sqrt {3}}-\sqrt {1-\text {$\#$1}} \sqrt {3 \text {$\#$1}-2}\&\right ][-2 x+c_1] \\ y(x)\to \text {InverseFunction}\left [\frac {\arctan \left (\frac {\sqrt {3 \text {$\#$1}-2}}{\sqrt {3-3 \text {$\#$1}}}\right )}{\sqrt {3}}-\sqrt {1-\text {$\#$1}} \sqrt {3 \text {$\#$1}-2}\&\right ][2 x+c_1] \\ y(x)\to 1 \\ \end{align*}