Internal problem ID [7598]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y^{2}-3 y+4=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve(diff(y(x),x) - y(x)^2 -3*y(x) + 4=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {4 \,{\mathrm e}^{5 x} c_{1}+1}{-1+{\mathrm e}^{5 x} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.571 (sec). Leaf size: 32
DSolve[y'[x] - y[x]^2 -3*y[x] + 4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-3-5 \coth \left (\frac {5 (x+c_1)}{2}\right )\right ) \\ y(x)\to -4 \\ y(x)\to 1 \\ \end{align*}