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Solve the following differential equations, 1) V1+x* y-3xVy-1=0. An

Solve the following differential equations, 1) V1+x* y-3xVy-1=0. An

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1- Separable variables differential equations Problems: Solve the following differential equations, 1) V1+x*.y' -3xVy² –1=0. 2) 2yy' = x(1- 2y), y(1) = 1. Ans.: y= cosh(3v1+x +C). Ans.: x +2y+In(2y-1) 3. x-3 3) (x - 4) y' = x(1-2y), y(5)=1. Ans.: y=- 2(x -4) 4) 2(1+x)(1+ y).y' +(y+2)? = 0. 2 =C- In(l+x). y+2 Ans.: 2 In(y + 2) + %3D 5) (1+3y).y' + 2y In(l+ x) = 0. Ans.: 2 In y +3 y = 4x-4(1+x)In(l + x) +C. %3D 6) (1+x) yy'- x(1 + y+ y') 0. 1+x 2 tan 1+2y C. Ans.: In 7) (1-xy+x'y')dx (x-x'y)dy. 8) (1+e20)dp + 2e20 d0 = 0. 9) tan (x+ y)dx-dy 0. 1+ y+ y 3 Ans.: x= Ce"-y? /2 Ans.: e" (1+e20)=C. Ans.: 2(x-y)-sin 2(x+ y) = C.
Transcribed Image Text:1- Separable variables differential equations Problems: Solve the following differential equations, 1) V1+x*.y' -3xVy² –1=0. 2) 2yy' = x(1- 2y), y(1) = 1. Ans.: y= cosh(3v1+x +C). Ans.: x +2y+In(2y-1) 3. x-3 3) (x - 4) y' = x(1-2y), y(5)=1. Ans.: y=- 2(x -4) 4) 2(1+x)(1+ y).y' +(y+2)? = 0. 2 =C- In(l+x). y+2 Ans.: 2 In(y + 2) + %3D 5) (1+3y).y' + 2y In(l+ x) = 0. Ans.: 2 In y +3 y = 4x-4(1+x)In(l + x) +C. %3D 6) (1+x) yy'- x(1 + y+ y') 0. 1+x 2 tan 1+2y C. Ans.: In 7) (1-xy+x'y')dx (x-x'y)dy. 8) (1+e20)dp + 2e20 d0 = 0. 9) tan (x+ y)dx-dy 0. 1+ y+ y 3 Ans.: x= Ce"-y? /2 Ans.: e" (1+e20)=C. Ans.: 2(x-y)-sin 2(x+ y) = C.
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