use the laplace transform to solve the given initial value problems c. ty" +y' + ty = 0; y(0) = 1, y'(0) = 0 ?? 5.

Q: y = In (x* + 5)³

A:

Q: 1. a) Find the successive derivatives of the following functions: (x' +80x²)* ii) Z (x* +10x +20) 21…

A:

Q: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

A:

Q: 8) Suppose y log3(xy) = y² – 6x. 8.1) Find at (1,3) 8.2) Find the tangent line to the curve at (1,3)

A:

Q: ху a) y'=Xy х +1

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: 6. If g(x) = x'+x²+ g"(2). find the value of

A: see 2nd step.

Q: Classify the following ODE y(4) -3y (3)-y' =0

A: We have to classify the ode

Q: 4. Find y' where y = – 1)^(2x – 1)3

A:

Q: 3. Find the value(s) of k for which y = e satisfies the equation y+2y' = y" derivative) (note: y" is…

A: k = 1+2, 1-2explanation is given in below step

Q: If a space shuttle's downward acceleration is given by y"(t) = –32 ft/s², find the osition function…

A:

Q: 5. Evaluate tan (x)sec'(x)dx

A: Find the integral by using substitution

Q: x²yy' = (y² - 1)3/2

A: Given that, x2yy'=y2-132 We can solve this by using variable separable method. ∫xn dx=xn+!n+1+C

Q: Find the derivative of 4x - 9y = 17 9x y' = 4y -4x y' = 9y 9x 4y 4x 9y

A: Given problem:- Find the derivative of 4x² - 9y² = 17

Q: The slope of the line tangent to the graph of 3x +5In y 12 at (2, 1) is 12 (A) 12 (B) 5. (C) 12 4.

A: Given that 3x2+5lny=12To find : Slope of the tangent line at point 2,1Solution :

Q: Find the general equation for y if y': √8x +3

A:

Q: 2. Let h'(2) = 8, h' (2) = 5, h(2) = 3, h″(4) = −—1,h'(4) 4 ª[₂x x.h"(x) dx. 3, h(4) 6. Find = =

A:

Q: 5. A termite population begins with 150 termites and increases at a rate of m'(t) termites per week.…

A: Termite population starts with 150 termites and increases with the rate of m'(t) termites per week

Q: Let 2² + y? = 1 and y(0) = 1 Then y'(0)= none of the listed here 1 -1

A:

Q: By= In(Cx-2)

A:

Q: 3. y = In(sec(In 0)) Find the derivation

A:

Q: 1 and y' CO)

A:

Q: q2-  91.2% of 1980 is: Select one: 18057.6 180576 180.576 1805.76 18.0576

A: We are asking to find 91.2% 0f 1980

Q: 24. What does it mean to say that dV is an exact differential?

A: What do you mean by dV is an exact differential.

Q: 19. Calculate: -12e* (b) (25t – 8e') el-3 dt (a) dt (c) dx Hint for (c): Write e'-3 as e-³e'.

A:

Q: 1. y' = 2(3x + y)? – 1; y(0) = 1

A: Given that: y'=2(3x+y)-1, y(0)=1

Q: 61. Show that the differential equations y' = 3y/x and y' = -x/3y define orthogonal families of…

A:

Q: solve the following ODE y + xy = 6xfy

A: We have y'+xy=6xy This can be written as: 1ydydx+xy=6x               ...(1) Let 1y=t So, we get:…