Internal problem ID [4621]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+x +y^{2} x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 14
dsolve([diff(y(x),x)+x+x*y(x)^2=0,y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = -\tan \left (\frac {x^{2}}{2}-\frac {1}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.348 (sec). Leaf size: 17
DSolve[{y'[x]+x+x*y[x]^2==0,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan \left (\frac {1}{2} \left (1-x^2\right )\right ) \\ \end{align*}