Internal problem ID [10885]
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).
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {{y^{\prime }}^{2} \sqrt {y}-\sin \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 58
dsolve(diff(y(x),x)^2*sqrt(y(x))=sin(x),y(x), singsol=all)
\begin{align*} \frac {4 y \left (x \right )^{\frac {5}{4}}}{5}+\int _{}^{x}-\frac {\sqrt {\sqrt {y \left (x \right )}\, \sin \left (\textit {\_a} \right )}}{y \left (x \right )^{\frac {1}{4}}}d \textit {\_a} +c_{1} = 0 \\ \frac {4 y \left (x \right )^{\frac {5}{4}}}{5}+\int _{}^{x}\frac {\sqrt {\sqrt {y \left (x \right )}\, \sin \left (\textit {\_a} \right )}}{y \left (x \right )^{\frac {1}{4}}}d \textit {\_a} +c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.269 (sec). Leaf size: 77
DSolve[y'[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*}