Find the exact solution of the given initial value problem, then apply Euler's method.Q. no. 12 only A programmable calculator or a computer will be useful forProblems 11 through 16. In each problem find the exact so-lution of the given initial value problem. Then apply Euler'smethod twice to approximate (to four decimal places) this so-lution on the given interval, first with step size h = 0.01, thenwith step size h = 0.005. Make a table showing the approxi-mate values and the actual value, together with the percentageerror in the more accurate approximation, for x an integralmultiple of 0.2. Throughout, primes denote derivatives withrespect to x.11. y' = y – 2, y(0) = 1;0 S x SI12. y' = }v – 1)², y(0) = 2;0 < x S 113. yy' = 2x³, y(1) = 3; 1 < x < 214. xy' = y², y(1) = 1; 1 < x < 215. xy' = 3x – 2y, y(2) = 3; 2 < x<316. y²y' = 2x$, y(2) = 3;2 < x S 3

Suppose we have a differential equation y'=fx,y, yx0=y0. Then according to Euler's method, the…

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Find the exact solution of the given initial value problem, then apply Euler's method

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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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

Find the exact solution of the given initial value problem, then apply Euler's method. Q. no. 12 only

A programmable calculator or a computer will be useful for
Problems 11 through 16. In each problem find the exact so-
lution of the given initial value problem. Then apply Euler's
method twice to approximate (to four decimal places) this so-
lution on the given interval, first with step size h = 0.01, then
with step size h = 0.005. Make a table showing the approxi-
mate values and the actual value, together with the percentage
error in the more accurate approximation, for x an integral
multiple of 0.2. Throughout, primes denote derivatives with
respect to x.
11. y' = y – 2, y(0) = 1;0 S x SI
12. y' = }v – 1)², y(0) = 2;0 < x S 1
13. yy' = 2x³, y(1) = 3; 1 < x < 2
14. xy' = y², y(1) = 1; 1 < x < 2
15. xy' = 3x – 2y, y(2) = 3; 2 < x<3
16. y²y' = 2x$, y(2) = 3;2 < x S 3

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