f(x) = 4x - 3 g(x) = 5x2 – 2 %3D f° g)(x) b. (g°f)(x) (f° g)(2) a. С.

Q: 8. (D2 – 10D + 34)y = -cos3x

A: Answer and explanation is given below

Q: Find, the genetal Solution of the differehtial equation (2x+Y-3) dy= (f+2Y-3)dX

A: Given problem:- Find the general Solution of the differential equation   (2x + y - 3) dy = (x + 2y -…

Q: 2 x b) sec dx 2

A: Evaluate the integral ∫π3π2sec2x2dx.

Q: 5 If [ f(x) dx = 18, then 5 (f(x) + 4) dx is equal to:

A: Using the properties of Integrals

Q: 3x² (- x) dx – (-y) dy = 0 2х (1) Find the general solution for

A: The given differential equation is: 2xy3-xdx-3x2y4-ydy=0 Comparing this with: M dx + N dy = 0, we…

Q: Solve the linear D.E dy = (e-X sec2x - y)dx

A: Given: dy=e-xsec2x-ydx ⇒dydx=e-xsec2x-y⇒dydx+y=e-xsec2x which is linear differential equation of the…

Q: Q3) Use Euler's method to estimate y(0.02) ey-x y' 1+ e2y •y(0) = 2 (h=0.01) .What is the error in…

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Q: The solution of (v + x + 5)dy = (v - x + 1) dx is

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Q: Solve it by linear D.E dy+2/x y.dx=4x.dx

A:

Q: 4.2(х — у)dx + (3х — у — 1)dy 3 0

A: Let's find.

Q: Evaluate each definite integral

A:

Q: dx :- x = ey/2 x3 dy 1- 2

A: First we need to reduce it into linear differential equation form by using substitution method

Q: (2x² – ye")dx – e dy = 0. - -

A:

Q: Identify f(x) to be used in variation of parameters to solve for y, e" y" + y' – 3y = x

A: To find f(x) write equation in form of y" + P y' +Q y = f(x).

Q: Obtain the general solution to the equation. 5. dx + (x – v²)dv = 0

A: Given that: dx+(x-y2)dy=0

Q: 2r-r2 -3 zVx2 + y2 dz dy dx. 0. 0.

A:

Q: If Sf(x)dx = 5, i f(x)dx = 2, and Sif(x) dx = -1, find f(x)dx. %3D %3D А.) -2 В.) 2 С.) -3 D.) 3

A:

Q: e-(2²+y²) dy dx x=-00 Jy=0

A: To evaluate the below integral. ∫x=−∞∞∫y=0∞e−x2+y2dydx

Q: If fe F dr = Sc(x - 2y³) dx + (x²y) dy, what is F?

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Q: (x + 2y – 1)dx + 3(x + 2y)dy = 0

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Q: Q2/ solve; A: dy - = e* * y3 dx x+1

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Q: dx (x-2)V4x²-16 is equal to 2 - -1 + C 4 sec

A:

Q: 3y" – 6y + 6y = e" sec x (variation of parameters) -

A: The given differential equation is 3y''-6y'+6y=exsecx to find the general solution using variation…

Q: -4x+2 Integrate f6 dx with respect to x using the substitution method. (-2x2+2a-2) COMPLETE THIS IN…

A:

Q: Solve the diffrencial equation.  4x3 y4 - Lny+(y/x)/-4x4 y3 + (x/y)-Lnx = dy/dx

A: Mdx + Ndy =0if ∂M∂y =∂N∂xIt's exact diffrential equation and then solution :∫y constMdx + ∫(terms of…

Q: 2 -e dy=x(xdy-ydx).

A:

Q: x+2 a) f- =dx V2x-x² |xIn(x+1)dx b)

A: Given that  (a) ∫(x+2)/√(2x-x2) dx   (b) ∫x ln(x+1)dx Here we have to calculate the given integral.

Q: Find the general solution: k^2 dx+(x-y+k)^2 dy3D0

A: Given that: k2dx+(x-y+k)2dy=0     NOTE: As per our answering guidelines, we can only answer 1…

Q: In the function given. Evaluate the integrals.

A: ∫36-3gxdx=∫36-3dx·∫36gxdx Also, ∫36gxdx=1

Q: Zx+1 8) I = - dx 7-7x+12

A:

Q: |(2 f(x)+3) dx=19 f(x)dx then equals?

A: ∫afx+bdx = a∫fxdx+∫bdx

Q: If f(x) dx = 3 and f(x) dx = 4 what is the value of %3D 5f(x) dx?

A:

Q: The f ²-3)³ dx is equal to x2

A: Given: I=∫x2-33x2dx For evaluating given integral, first we simplify given expression then integrate…

Q: Using the variation of parameters, find the particular solution of (D2 + 1)y = sec x

A:

Q: 6+ | f(x) dx = 21 and g(x) dx = 14, find (3f (x) + 5g(x)] dx.

A:

Q: Q3) Use Euler's method to estimate y(0.02) ey-x y' = 1+ e2y •Y(0) = 1 (h=0.01) .What is the error in…

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Q: e-(2²+x³) dy dæ x=-0 Jy=0

A:

Q: 2dy+ydx=y3(x-1)dx (Bernoulli)

A: We have to find the general solution of differential equations

Q: ;F · dř = Sc(-5æ + 4y³) dx + (x³y) dy, what is F?

A: In this question, the concept of line integral is applied. Line Integral The function to be…

Q: using variation of parameters: - 2x + x = e t (et 1 1)2

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Q: 8.) Find of y3 = x* + 3x d?y dx2

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Q: 6- 2 dx 子 メt Casy =0.

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Q: Find and in terms of t. dx2 x= -9 sint, y = cost dx dx2

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Q: 3 c2x S *x² dy dx 4.

A: Integral

Q: (d) y = x* (e) y = In(e2r + e-2#) (f) f(r) = e-

A: See solution below

Q: (x-G -0 +2) dx + 2(x+2y+2) dy:

A:

Q: f(x)dx=10 and | f(x)dx=3, then f(4 – x)dx=?

A: topic - properties of integration

Q: dx 2. = 3x. dt

A: The given differential equation is                                                    dxdt=3x…

Q: 5. The solution of the eq. xy?dy - (x³ + y³)dx = 0 is Ln(2v3 – 1) + Lnx = c F

A: F

Q: 4x (e) Find -dx .2 Vx² +4

A: