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Solving Differential Equations, Exercises of Differential Equations

Massachusetts Institute of Technology (MIT)Differential Equations

Exercises on solving differential equations. It includes finding solutions for different types of differential equations, such as y'=x and y'=sin(x)+x^5+ln(x). It also shows how to verify if a given function is a solution of a differential equation. The exercises are suitable for university students studying calculus and differential equations.

Typology: Exercises

2021/2022

Uploaded on 05/11/2023

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Differential Equations
1. (a) Find some solutions of the differential equation y0=x.
(b) Find some solutions of the differential equation y0=1
2(x2
−1).
(c) Find some solutions of the differential equation y0= sin(x) + x5+ ln(x).
2. Find some solutions of the differential equation y0=y.
3. (a) Show that each of the following functions
1 + cet
1−cet
is a solution of the differential equation y0=1
2(y2
−1).
1
pf2

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1. (a) Find some solutions of the differential equationDifferential Equations y′^ = x.

(b) Find some solutions of the differential equation y′^ = 12 (x^2 − 1). (c) Find some solutions of the differential equation y′^ = sin(x) + x^5 + ln(x).

  1. Find some solutions of the differential equation y′^ = y.
  2. (a) Show that each of the following functions 1 + 1 − cecett is a solution of the differential equation y′^ = 12 (y^2 − 1). 1

(b) Find a solution of this differential equation that satisfies the initial condition y(0) = 2.