The solution of the IVP y" – 3y' – 4y = 0, y(0) = 0, v'(0) = 5 is: Select one: а. y = e4t - e-t O b. y = - e-41 + e' O C. y = - e4t + e-t d. Y= e-4 - et

Q: ds if s = Find dt 7t + 3 ds dt II

A: We have given;

Q: Calculate y" and y'''. y = 4t 3 - 9t 2 + 7

A: Given that  y = 4t3 - 9t2 + 7 We have to calculate y'' and y'''. First we find y'. y' = ddty     =…

Q: y" - 3y' + 2y = 2x² + ex + 2xe* + 4e³x

A:

Q: If x²y + 3y* = xtan(y) + 2x d²y Find the value of dx²"

A:

Q: y" - 7y' + 12y = 0

A: We have to solve  y" - 7y' + 12y = 0 (D2 - 7D + 12)y = 0 The auxiliary equation is

Q: Solve ,  y" - 6y' + 8y = 0

A: Given differential equation; y" - 6y' + 8y = 0

Q: 9-y" - 2y +2y=e; y(0) = 0, y(0) = 1

A:

Q: If y=5+ V3x +1, find y' when x = 5. 1 А. 13 В. C. 15 D. 16

A: Given,    y=5+3x+1

Q: y" + xy' = 0, x0=0

A:

Q: (3x² – 2xy + 3y²)dx = 4xy dy

A: 6. The given is  3x2-2xy+3y2dx=4xydy Thus, dydx=3x2-2xy+3y24xy.....(1) which is a homogeneous…

Q: y²-6x²y=-9x ; y' at (1,3)

A:

Q: ду Find ду and when dz (a) y = 6 + 3x + 16z + 4x2 + 2z2 (b) y = 14x2 (c) y = 9 + 4xz - 3x2 %3D

A:

Q: Eliminate the arbitrary constant. y=Ax 5 + Bx3

A:

Q: 9y" + 30y' + 25y = 0, and y(3) = 9, y (3) = 3. %3D

A: For the complementary solution consider the quadratic  9m2+30m+25=0 The equation has repeated roots…

Q: Solve zx+zzy= 2x, z(0, y) = y

A:

Q: xy' + y + 2y' - xsinx = 2sinx

A:

Q: = VI3(t G-÷) A W = w? = 5 – 12i, w e C w= ±v13 (은+i) B 13 13 V13 (+ w = W 13 13 w = ±V13(1+ 2i) D w=…

A:

Q: Separate the equation (1 + x + y + xy)y' =x.

A: First, convert the expression on the left-hand side in product form and then separate the equation…

Q: Determine u and du. Show solution

A:

Q: Determine the equation whose y'= Y/3x. 3x2 = y3 A 1 у? y= 3 x2 © x² = y3 1

A:

Q: %3D у — Зу + Зу - у %3D 4е" y y =

A:

Q: Solve the equation: y" -y = 2* + Oy=ce to xe +e* (x+c3e2X + CA) Oy=c₁e* + c₂e* + ex (x + c3e-²x +…

A:

Q: 4. Find y': y = 3x7 – 14x6 + 42 %3D

A: Given that:   y=3x7-14x6+42

Q: Solve:  y’’’ – 4y’’ + y’ + 6y = 0

A:

Q: y" + y' - 6y = ex - 2

A:

Q: 3.y=1x² -2x リ=(x-2x)。 dy=$(x²-2x)*x (2x-2) -2x) 12 (2x-2 %3D /2-) メ 2メ-2 d メ-

A:

Q: (2ху-у*+у)dx + (3x*-4ху+3x)dy D0 %3D

A:

Q: y = 8. w = (sin 0)® 9. е* + еУ %3D е**у 7. у%3D 3*x3 ex+y 10. xY + 2* – 4 = 0

A:

Q: (2х + Зу — 5)dx + (3x — у — 2)dy — 0

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.