Question

1.5 Problems Find general solutions of the differential equations in Problems 1 through 25. If an initial condition is given, find the corresponding particular solution. Throughout, primes denote derivatives with respect to $x$. 1. $y' + y = 2$, $y(0) = 0$ 3. $y' + 3y = 2xe^{-3x}$ 5. $xy' + 2y = 3x$, $y(1) = 5$ 6. $xy' + 5y = 7x^2$, $y(2) = 5$ 7. $2xy' + y = 10\sqrt{x}$ 2. $y' - 2y = 3e^{2x}$, $y(0) = 0$ 4. $y' - 2xy = e^{x^2}$ 8. $3xy' + y = 12x$

          1.5 Problems
Find general solutions of the differential equations in Problems 1 through 25. If an initial condition is given, find the corresponding particular solution. Throughout, primes denote derivatives with respect to $x$.
1. $y' + y = 2$, $y(0) = 0$
3. $y' + 3y = 2xe^{-3x}$
5. $xy' + 2y = 3x$, $y(1) = 5$
6. $xy' + 5y = 7x^2$, $y(2) = 5$
7. $2xy' + y = 10\sqrt{x}$
2. $y' - 2y = 3e^{2x}$, $y(0) = 0$
4. $y' - 2xy = e^{x^2}$
8. $3xy' + y = 12x$

1.5 Problems
Find general solutions of the differential equations in Problems 1 through 25. If an initial condition is given, find the corresponding particular solution. Throughout, primes denote derivatives with respect to x.
1. y' + y = 2, y(0) = 0
3. y' + 3y = 2xe^-3x
5. xy' + 2y = 3x, y(1) = 5
6. xy' + 5y = 7x^2, y(2) = 5
7. 2xy' + y = 10√(x)
2. y' - 2y = 3e^2x, y(0) = 0
4. y' - 2xy = e^x^2
8. 3xy' + y = 12x

Added by Maria G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Heba Qureshi

Step 1

y' + y = 2, y(0) = 0 To solve this first-order linear differential equation, we can use an integrating factor. The integrating factor is e^(∫1 dx) = e^x. Multiply the equation by e^x: e^x y' + e^x y = 2e^x Now, notice that the left side is the derivative of the Show more…

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1.5 Problems: General Solutions of Differential Equations Find the corresponding particular solution for the given initial condition. Throughout, primes denote derivatives with respect to x. 1. y + y' = 2, y(0) = 0 2. y' - 2y + 3e^(2x), y(0) = 0 3. y + 3y' = 2xe^(-3x) 4. y - 2xy' + 2y = 0 5. xy + 2y = 3x, y(0) = 5 6. xy + Sy' = 7x^2, y(2) = 5 7. 2xy + y = âˆš(10x) 8. 3xy' + y = 12x