62.20.4 problem Ex 4

Internal problem ID [12918]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter V, Singular solutions. Article 33. Page 73
Problem number : Ex 4
Date solved : Tuesday, January 28, 2025 at 04:43:55 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.096 (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 &= 1 \\ x +\frac {y^{2} \left (y-1\right )}{\sqrt {-y \left (y-1\right )}}-c_{1} &= 0 \\ x -\frac {y^{2} \left (y-1\right )}{\sqrt {-y \left (y-1\right )}}-c_{1} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 60.226 (sec). Leaf size: 3751

DSolve[y[x]*(3-4*y[x])^2*D[y[x],x]^2==4*(1-y[x]),y[x],x,IncludeSingularSolutions -> True]
 

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