38.2.43 problem 43

Internal problem ID [6472]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 43
Date solved : Monday, January 27, 2025 at 02:07:04 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }+x +x y^{2}&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 14

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

\[ y = -\tan \left (\frac {x^{2}}{2}-\frac {1}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.255 (sec). Leaf size: 17

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

\[ y(x)\to \tan \left (\frac {1}{2} \left (1-x^2\right )\right ) \]