73.3.12 problem 4.4 (b)

Internal problem ID [15046]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.4 (b)
Date solved : Tuesday, January 28, 2025 at 07:28:32 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}+9 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 14

dsolve(diff(y(x),x)=y(x)^2+9,y(x), singsol=all)
 

\[ y = 3 \tan \left (3 c_{1} +3 x \right ) \]

✓ Solution by Mathematica

Time used: 0.197 (sec). Leaf size: 41

DSolve[D[y[x],x]==y[x]^2+9,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+9}dK[1]\&\right ][x+c_1] \\ y(x)\to -3 i \\ y(x)\to 3 i \\ \end{align*}