Internal problem ID [14172]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }=-2 \cos \left (9 t \right )-2 \sin \left (7 t \right )} \]
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 28
dsolve((5*x(t)^5-4*cos(x(t)))*diff(x(t),t)+(2*cos(9*t)+2*sin(7*t))=0,x(t), singsol=all)
\[ \frac {\sin \left (9 t \right )}{9}-\frac {\cos \left (7 t \right )}{7}+\frac {5 x \left (t \right )^{6}}{12}-2 \sin \left (x \left (t \right )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.667 (sec). Leaf size: 40
DSolve[(5*x[t]^5-4*Cos[x[t]])*x'[t]+(2*Cos[9*t]+2*Sin[7*t])==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \text {InverseFunction}\left [\frac {5 \text {$\#$1}^6}{6}-4 \sin (\text {$\#$1})\&\right ]\left [-\frac {2}{9} \sin (9 t)+\frac {2}{7} \cos (7 t)+c_1\right ] \]