Internal problem ID [5129]
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]
\[ \boxed {y^{\prime }+x y^{2}=-x} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([diff(y(x),x)+x+x*y(x)^2=0,y(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -\tan \left (\frac {x^{2}}{2}-\frac {1}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.215 (sec). Leaf size: 17
DSolve[{y'[x]+x+x*y[x]^2==0,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \tan \left (\frac {1}{2} \left (1-x^2\right )\right ) \]