60.1.17 problem 17

Internal problem ID [10031]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 17
Date solved : Monday, January 27, 2025 at 06:18:50 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-y^{2}-3 y+4&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 24

dsolve(diff(y(x),x) - y(x)^2 -3*y(x) + 4=0,y(x), singsol=all)
 

\[ y = \frac {-4 \,{\mathrm e}^{5 x} c_{1} -1}{{\mathrm e}^{5 x} c_{1} -1} \]

✓ Solution by Mathematica

Time used: 0.218 (sec). Leaf size: 42

DSolve[D[y[x],x] - y[x]^2 -3*y[x] + 4==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) (K[1]+4)}dK[1]\&\right ][x+c_1] \\ y(x)\to -4 \\ y(x)\to 1 \\ \end{align*}