Internal problem ID [3273]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-x^{2} \left (a \,x^{3}+y b \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x) = x^2*(a*x^3+b*y(x)),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x^{3} a}{b}-\frac {3 a}{b^{2}}+{\mathrm e}^{\frac {b \,x^{3}}{3}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 32
DSolve[y'[x]==x^2*(a*x^3+b*y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {a \left (b x^3+3\right )}{b^2}+c_1 e^{\frac {b x^3}{3}} \]