44.5.67 problem 57

Internal problem ID [7129]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 57
Date solved : Tuesday, February 04, 2025 at 12:25:13 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sqrt {1+y^{2}}\, \sin \left (y\right )^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.839 (sec). Leaf size: 31

dsolve([diff(y(x),x)=sqrt(1+y(x)^2)*sin(y(x))^2,y(0) = 1/2],y(x), singsol=all)
 

\[ y = \operatorname {RootOf}\left (2 \left (\int _{\frac {1}{2}}^{\textit {\_Z}}\frac {1}{\sqrt {\textit {\_a}^{2}+1}\, \left (-1+\cos \left (2 \textit {\_a} \right )\right )}d \textit {\_a} \right )+x \right ) \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[y[x],x]==Sqrt[1+y[x]^2]*Sin[y[x]]^2,{y[0]==1/2}},y[x],x,IncludeSingularSolutions -> True]
 

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