2.43 problem 43

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*}