44.1.8 problem 9
Internal
problem
ID
[6883]
Book
:
A
First
Course
in
Differential
Equations
with
Modeling
Applications
by
Dennis
G.
Zill.
12
ed.
Metric
version.
2024.
Cengage
learning.
Section
:
Chapter
1.
Introduction
to
differential
equations.
Exercises
1.1
at
page
12
Problem
number
:
9
Date
solved
:
Sunday, March 30, 2025 at 11:26:30 AM
CAS
classification
:
[[_homogeneous, `class C`], _dAlembert]
\begin{align*} \sin \left (y^{\prime }\right )&=y+x \end{align*}
✓ Maple. Time used: 0.031 (sec). Leaf size: 38
ode:=sin(diff(y(x),x)) = x+y(x);
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= -\sin \left (1\right )-x \\
y &= \sin \left (-1+\operatorname {RootOf}\left (-x +\operatorname {Si}\left (\textit {\_Z} \right ) \sin \left (1\right )+\operatorname {Ci}\left (\textit {\_Z} \right ) \cos \left (1\right )+c_1 \right )\right )-x \\
\end{align*}
✓ Mathematica. Time used: 16.078 (sec). Leaf size: 324
ode=Sin[D[y[x],x]]==y[x]+x;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\int _1^{y(x)}\left (\frac {\cos (1) \sqrt {1-(x+K[1])^2} \cos (\arcsin (x+K[1])+1)}{2 (\arcsin (x+K[1])+1) (x+K[1]-1)}-\frac {\cos (1) \sqrt {1-(x+K[1])^2} \cos (\arcsin (x+K[1])+1)}{2 (\arcsin (x+K[1])+1) (x+K[1]+1)}+\frac {\arcsin (x+K[1]) \sqrt {1-(x+K[1])^2} \sin (1) \text {sinc}(\arcsin (x+K[1])+1)}{2 (\arcsin (x+K[1])+1) (x+K[1]-1)}+\frac {\sqrt {1-(x+K[1])^2} \sin (1) \text {sinc}(\arcsin (x+K[1])+1)}{2 (\arcsin (x+K[1])+1) (x+K[1]-1)}-\frac {\arcsin (x+K[1]) \sqrt {1-(x+K[1])^2} \sin (1) \text {sinc}(\arcsin (x+K[1])+1)}{2 (\arcsin (x+K[1])+1) (x+K[1]+1)}-\frac {\sqrt {1-(x+K[1])^2} \sin (1) \text {sinc}(\arcsin (x+K[1])+1)}{2 (\arcsin (x+K[1])+1) (x+K[1]+1)}+\frac {1}{\arcsin (x+K[1])+1}\right )dK[1]+\cos (1) \operatorname {CosIntegral}(\arcsin (x+y(x))+1)+\sin (1) \text {Si}(\arcsin (x+y(x))+1)-x=c_1,y(x)\right ]
\]
✓ Sympy. Time used: 3.949 (sec). Leaf size: 80
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-x - y(x) + sin(Derivative(y(x), x)),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = C_{1} + x - \int \limits ^{- C_{2} - x} \frac {\operatorname {asin}{\left (r \right )}}{\operatorname {asin}{\left (r \right )} + 1 + \pi }\, dr - \pi \int \limits ^{- C_{2} - x} \frac {1}{\operatorname {asin}{\left (r \right )} + 1 + \pi }\, dr + \int \limits ^{- C_{2} - x} \frac {1}{\operatorname {asin}{\left (r \right )} + 1 + \pi }\, dr, \ y{\left (x \right )} = C_{1} + x - \int \limits ^{- C_{2} - x} \frac {\operatorname {asin}{\left (r \right )}}{\operatorname {asin}{\left (r \right )} - 1}\, dr - \int \limits ^{- C_{2} - x} \frac {1}{\operatorname {asin}{\left (r \right )} - 1}\, dr\right ]
\]