40.6.8 problem 17

Internal problem ID [6688]
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
Date solved : Monday, January 27, 2025 at 02:22:26 PM
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: 0.027 (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: 60.483 (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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