67.2.12 problem Problem 1(L)

Internal problem ID [13969]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 1(L)
Date solved : Tuesday, January 28, 2025 at 06:10:37 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} {y^{\prime }}^{2} \sqrt {y}&=\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.971 (sec). Leaf size: 58

dsolve(diff(y(x),x)^2*sqrt(y(x))=sin(x),y(x), singsol=all)
 

\begin{align*} \frac {4 y^{{5}/{4}}}{5}-\frac {\int _{}^{x}\sqrt {\sqrt {y}\, \sin \left (\textit {\_a} \right )}d \textit {\_a}}{y^{{1}/{4}}}+c_{1} &= 0 \\ \frac {4 y^{{5}/{4}}}{5}+\frac {\int _{}^{x}\sqrt {\sqrt {y}\, \sin \left (\textit {\_a} \right )}d \textit {\_a}}{y^{{1}/{4}}}+c_{1} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.249 (sec). Leaf size: 77

DSolve[D[y[x],x]^2*Sqrt[y[x]]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {5^{4/5} \left (-2 E\left (\left .\frac {1}{4} (\pi -2 x)\right |2\right )+c_1\right ){}^{4/5}}{2\ 2^{3/5}} \\ y(x)\to \frac {5^{4/5} \left (2 E\left (\left .\frac {1}{4} (\pi -2 x)\right |2\right )+c_1\right ){}^{4/5}}{2\ 2^{3/5}} \\ \end{align*}