Question

In: Math

Solve the following first order differential equations: (a) 2/?^ ???/?? = 4?^2? ; ?(0) = −1/...

Solve the following first order differential equations:

(a) 2/?^ ???/?? = 4?^2? ; ?(0) = −1/ 3

(b) ??/?? + ? = ? ; ?(0) = 5

(c) ??/?? + ? /? = ? 3 ; ? ( 1/2 ) = 1

Solutions

Expert Solution

a) This Differential equation can be solved by isolating y'.

b)Use ODE form to solve the Differential equation.

c) Use ODE form to solve the Differential equation.


Related Solutions

using series to solve differential equations using series to solve differential equations 1.) y’’-(e^5x)y’+xy=0,y(0)=2,y’(0)=1
using series to solve differential equations using series to solve differential equations 1.) y’’-(e^5x)y’+xy=0,y(0)=2,y’(0)=1
1. Use Laplace transforms to solve the following differential equations for ?(?) for ? ≥ 0....
1. Use Laplace transforms to solve the following differential equations for ?(?) for ? ≥ 0. Use ?(0) = 0 and ?̇(0) = 1 for each case. i. 0 = ?̈(?) + 2?̇(?) + 4?(?) ii. 0 = ?̈(?) + 3?̇(?) + 2?(?) iii. 5 = ?̈(?) + 5?̇(?) + 6?(?) 3. For the three differential equations from problem one determine the steady-state value of the system using: a. lim?→0 ??(?), b. lim ?→∞ ?(?) analytically, c. lim ?→∞ ?(?)...
Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where...
Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where x=[x(t)y(t)]. x(t)= y(t)= please be as clear as possible especially when solving for c1 and c2 that's the part i need help the most
Solve the given system of differential equations. ??/?? = ? + 4? ??/?? = ? +...
Solve the given system of differential equations. ??/?? = ? + 4? ??/?? = ? + y
I need the matlab codes for following question (1) (a). Solve the following second-order differential equations...
I need the matlab codes for following question (1) (a). Solve the following second-order differential equations by a pair of first-order equations, xyʹʹ − yʹ − 8x3y3 = 0; with initial conditions y = 0.5 and yʹ = −0.5 at x = 1. (b). Solve the problem in part (a) above using MATLAB built-in functions ode23 and ode45, within the range of 1 to 4, and compare with the exact solution of y = 1/(1 + x2) [Hint: ode23 à...
Write the second order differential equation as a system of two linear differential equations then solve...
Write the second order differential equation as a system of two linear differential equations then solve it. y" + y' - 6y = e^-3t y(0) =0   y'(0)=0
Differential Equations 22. Solve each of the following systems of equations. (c) (D-2)x=0; -3x+(D+2)y=0; -2y+(D-3)z=0 I...
Differential Equations 22. Solve each of the following systems of equations. (c) (D-2)x=0; -3x+(D+2)y=0; -2y+(D-3)z=0 I got x=c1e2t, y= 3/4 C1e2t + C2e-2t by using diffieq method d/dx(ye2t) = 3C1e2t....., but the right answer is x=4c1e2t, y= 3C1e2t + 5C2e-2t , z= -6C1e2t -2C2e-2t+C3e3t I want to know where 4 came from, and please do not use matrix system.
1) Solve each of the following differential equations. a)16y"-8y'+y=0 b) (d^4y)/(dx^4)-13((d^2y)/(dx^2))+36y=0 2) use Variation of Parameters...
1) Solve each of the following differential equations. a)16y"-8y'+y=0 b) (d^4y)/(dx^4)-13((d^2y)/(dx^2))+36y=0 2) use Variation of Parameters to solve y"+16y=(1/3)csc4t 3) use undetermined coefficients to solve y"-5y'+4y=3e^(3t)-5e^(2t) with y'(0)=-1 and y(0)=1 4) Explain why the product (A+B)(A-B) not equal A^2-B^2 fro two NXN matrices A and B. what is the product of (A+B)(A-B)?
Solve the following differential equations using Taylor series centered at 0. It’s enough to find the...
Solve the following differential equations using Taylor series centered at 0. It’s enough to find the recurrence relation and the first 3 terms of the series. (a) y''− 2y' + y = 0 (b) y'' + xy' + 2y = 0 (c) (2 + x^2 )y'' − xy'+ 4y = 0
Solve the following differential equations. a.) (2xy^2 +2x)dx−(4x^2 +1)dy=0 b.) (3ye^(3xy) +4xy)dx+(3xe^(3xy) +2x^2)dy=0
Solve the following differential equations. a.) (2xy^2 +2x)dx−(4x^2 +1)dy=0 b.) (3ye^(3xy) +4xy)dx+(3xe^(3xy) +2x^2)dy=0
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT