67.2.12 problem Problem 1(L)

Internal problem ID [13898]
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 : Monday, March 31, 2025 at 08:17:23 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*}

✓ Maple. Time used: 0.190 (sec). Leaf size: 58

ode:=diff(y(x),x)^2*y(x)^(1/2) = sin(x); 
dsolve(ode,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*}

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

ode=D[y[x],x]^2*Sqrt[y[x]]==Sin[x]; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 1.650 (sec). Leaf size: 58

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sqrt(y(x))*Derivative(y(x), x)**2 - sin(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ \left (\frac {4 y{\left (x \right )}}{5} + \int \sqrt {\frac {\sin {\left (x \right )}}{\sqrt {y{\left (x \right )}}}}\, dx\right ) \sqrt [4]{y{\left (x \right )}} = C_{1}, \ \left (\frac {4 y{\left (x \right )}}{5} - \int \sqrt {\frac {\sin {\left (x \right )}}{\sqrt {y{\left (x \right )}}}}\, dx\right ) \sqrt [4]{y{\left (x \right )}} = C_{1}\right ] \]