74.4.14 problem 14

Internal problem ID [15907]
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
Date solved : Tuesday, January 28, 2025 at 08:18:17 AM
CAS classification : [_separable]

\begin{align*} \left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.239 (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: 0.560 (sec). Leaf size: 50

DSolve[(5*x[t]^5-4*Cos[x[t]])*D[x[t],t]+(2*Cos[9*t]+2*Sin[7*t])==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\left (5 K[1]^5-4 \cos (K[1])\right )dK[1]\&\right ]\left [\int _1^t-2 (\cos (9 K[2])+\sin (7 K[2]))dK[2]+c_1\right ] \]