Q5 Suppose the equation y" – 4y' – 5y =f (x) has y = 3x' as a solution. (a) Find f (x). (b) What is the general solution of the equation? (c) Given that y(0) = 3 and y'(0) = 3, solve the initial value problem.

Q: (c) A function y(t) is a solution of y' + ky = 0. Sup find: (i) k (ii) y(t)

A: It is differential equation problem

Q: Solve the initial value problem. -7 4 y' = у, у(0): -6 7 -4 |

A:

Q: Q33. Solve the differential equation 5 xz (a) y3 = +c 5 (b) y³ = + c 1 x√x 5 (c) y³ = √x + c< 5 5…

A:

Q: The unique solution to the initial value problem is y(t) = 8e-5t - 2t + 9. Determine the constant yo…

A:

Q: B1(b): Solve the initial value problem : f'(x)= x!0 + 12x + 19 and f(0) = 1.

A:

Q: Solve initial value problem f'(x) = x³ – 8x2 + 16x + 1;f(0) = 0.

A:

Q: Solve the IVP g'(x) = (x² - 2x + 3)e-, and g(0) = 0.

A: NOTE: Refresh your page if you can't see any equations. . take integration on both sides

Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: ) Solve for the general solution of the equation: 2x’’+ 200x = 0 B) Solve for the particular…

A:

Q: Solve the initial value problem : f'(x) = x1® – 4x² + 12x + 13 and f(0) = 2. %3D

A: The given equation is, f'(x)=x16-4x2+12x+13 and f(0)=2. Integrate the given function as shown below.…

Q: Solve the initial value problem = 2Vi, y(1) = 4. (Use symbolic notation and fractions where needed.)…

A:

Q: 6. Solve the initial value problem: (2² + 2y^) Jy dx = xy, y(-1) = 1

A:

Q: (h) xy" + 8y' +18xy = 0, xo = 1 (i) (3 — x²)y" — 8xy' - 18y = 0, xo = 0 (j) 2y" + 8xy' + 18y = 0, xo…

A:

Q: 5 || I2 = Solve the following initial value problem: 5 -4 d ² = (₁ = 3 ) * dt 4 - + 18e³t 12 z (0) =…

A: Given system is    ,                         Let   then we get the above system…

Q: The family of functions is solution of the equation y = ce -21 te-² y' + 2y = e. Find the constant c…

A:

Q: B1(b): Solve the initial value problem f'(x) = x11 + 12x + 14 and f(0) = 2.

A:

Q: Solve the initial value problem x2(dy/dx)=(3x2-x-5)/(x+1)(y+1), y(1)=2

A:

Q: y" + 9y = 40e*; y(0) = 5, y'(0) = -2.

A:

Q: Find f by solving the initial-value problem. f'(x) = 6x² + 6x - 9; f(2)= 2 f(x) =

A:

Q: 4. (a) dzy Solve: dx2 + ( = 0. (b) Solve xy" + (1 – x)y' – 2(1+x)y = e-*(1 – 6x) by the method based…

A: We have, d2ydx2+dydx+dydx3=0 ..i Put dydx=v ⇒d2ydx2=dvdx Now substitute in equation i we get…

Q: Solve the initial value problem: 4y''-16y'+16y=0, y(-1)=-2e-2, y'(-1)=4e-2.

A: The characteristic equation of the differential equation 4y''-16y'+16y=0 is 4m2-16m+16=0 Now ,…

Q: Solve (D-2)²(D²+1) y=0,y (0)=1y '(0)=2, y'' (0)=3, y''' (0)=4

A:

Q: The general solution to the equation y'' + 4y' + 3y = 0 has the form c₁eat + c₂ebt where a < b. a =…

A: (a)  The given differential equation is                         y''+4y'+3y=0      The auxiliary…

Q: 2. Solve the initial value problem: 2 + 2y = 6e¬*;y(0) = 8 %3| dx

A: To solve given initial value problem first we solve for integrating factor for given first order…

Q: Solve u'(t)+u(t)=−5 subject to u(0)=1.

A:

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.