Internal problem ID [5345]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 10. Singular solutions, Extraneous loci. Supplemetary problems. Page
74
Problem number: 17.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y \left (3-4 y\right )^{2} {y^{\prime }}^{2}+4 y=4} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 58
dsolve(y(x)*(3-4*y(x))^2*diff(y(x),x)^2=4*(1-y(x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 1 \\ x +\frac {y \left (x \right )^{2} \left (y \left (x \right )-1\right )}{\sqrt {-y \left (x \right ) \left (y \left (x \right )-1\right )}}-c_{1} &= 0 \\ x -\frac {y \left (x \right )^{2} \left (y \left (x \right )-1\right )}{\sqrt {-y \left (x \right ) \left (y \left (x \right )-1\right )}}-c_{1} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.264 (sec). Leaf size: 3751
DSolve[y[x]*(3-4*y[x])^2*y'[x]^2==4*(1-y[x]),y[x],x,IncludeSingularSolutions -> True]
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