Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it into a linear equation. The most important such equation has the form y + p(t)y = q(t)y" and is called Bernoulli's equation after Jakob Bernoulli. If n + 0, 1, then the substitution v = y- reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. fy + 2ry – y = 0, 1 >0 y = + V+ cr y =±1/- +c 5t y =+V3 + ct 1 y = + I+ ce 31

Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it into a linear equation. The most important such equation has the form y + p(t)y = q(t)y" and is called Bernoulli's equation after Jakob Bernoulli. If n + 0, 1, then the substitution v = y- reduces Bernoulli's equation to a linear equation. Solve the given Bernoulli equation by using this substitution. fy + 2ry – y = 0, 1 >0 y = + V+ cr y =±1/- +c 5t y =+V3 + ct 1 y = + I+ ce 31

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Sometimes it is possible to solve a nonlinear equation by making a change of the dependent variable that converts it into a linear equation. The most important such equation has the form
y + p(t)y = q(t)y"
and is called Bernoulli's equation after Jakob Bernoulli.
If n + 0, 1, then the substitution v = y'-* reduces Bernoulli's equation to a linear equation.
Solve the given Bernoulli equation by using this substitution.
Py + 2ty – y = 0, t >0
1
y = +
+ ct
V 51
5t
+cf
3t
y3+
1
y =+
+ cr²
V

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