Internal problem ID [13372]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page
103
Problem number: 5.3 (f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }-x \left (3+3 x^{2}-y\right )=0} \] With initial conditions \begin {align*} [y \left (2\right ) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([(1+x^2)*diff(y(x),x)=x*(3+3*x^2-y(x)),y(2) = 8],y(x), singsol=all)
\[ y \left (x \right ) = x^{2}+1+\frac {3 \sqrt {5}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 26
DSolve[{(1+x^2)*y'[x]==x*(3+3*x^2-y[x]),{y[2]==8}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2+\frac {3 \sqrt {5}}{\sqrt {x^2+1}}+1 \]