73.7.45 problem 45

Internal problem ID [15203]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 45
Date solved : Tuesday, January 28, 2025 at 07:42:01 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{4 x +3 y} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 26

dsolve(diff(y(x),x)=exp(4*x+3*y(x)),y(x), singsol=all)
 

\[ y = -\frac {\ln \left (3\right )}{3}+\frac {2 \ln \left (2\right )}{3}-\frac {\ln \left (-{\mathrm e}^{4 x}-4 c_{1} \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.880 (sec). Leaf size: 24

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

\[ y(x)\to -\frac {1}{3} \log \left (-\frac {3}{4} \left (e^{4 x}+4 c_1\right )\right ) \]