1. y = 5u°; u=7x – 4x' + 2x –9 2х-9 u +1. u=Vx? +1 y = u? -1' 3. x=7y -3y +y +8 2.

Q: dt cos²(t) dr du du cos? (t) at + ex. -7u, dx ex dr du -7u slove dr t (0 ) -0, x(0 ) -λ , u (0)-eet…

A:

Q: y" + 2y + 5y = t cos(5t)-6,y(0) = 1, y'(0) = -2

A: Here we use the table of Laplace transform and the partial fraction method to find solution.

Q: 9- Find the values of y(0.1) and (0.2) for Riccati equation y'= y + xy-1; y(0) = 0

A:

Q: y (1) = t+ y(t-t)cos rdt , y(0) = 0

A:

Q: 2. Compute dy dx (x² + y²)' by first changing it to polar coordinates.

A:

Q: Use the method of Frobenius to find solutions near x =0 of the following differentia equation dy…

A: Given that x2y''+xy'-x(x+1)y=0 Divide the equation with x2, y''+1xy'-1+1xy=0 Take y=∑n=0∞anxn+r Then…

Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

Q: y" + y = cos 2t + 28(t – T/2) – 38(t – 1), y(0) = 0, y'(0) = –1

A: Laplace transferom

Q: 5. Eliminate the parameter to find a Cartesian equation of the following curves. et (a) x = vt+1, y…

A: Eliminate parameter t.

Q: y" + 2y' + 5y = t cos(5t) - 6, y(0) = 1, y'(0) = -2

A: We can solve using Laplace transform

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 6, y = a sin 2 0 from e…

A:

Q: 16. y' + (2/t)y = (cos t)/t, y(n) 3D0, t> 0

A: The given DE is: y'+2ty=costt2

Q: (b) Given that cos (t) Vos(21) sin' (t) Jos(2)" |cos(2t) dy Find for the parametric equation given…

A:

Q: dy = cos 20. de dx Given that r= cos 0 ; = - sin 20 and de The slope of the tangent line to the…

A: Given that: r=cosθdxdθ=-sin2θdydθ=cos2θ

Q: 0 16) cos t dt dx

A: Given:

Q: b) y"+ 4 y = cos (t), y(0) = y'(0) = 0

A:

Q: 5. Find the equation of the tangent line to the curve given by the parametric equations x(t)= 3r² –…

A: We are authorized to solve only 1 question, please repost remaining questions Equation of tangent to…

Q: 4. y" + y = tan x. 5. 4y" – 4y' – 8y = 8e-t 6. y" – 2y + y = : + 3e 1+ t2 et 7. 4y" +y = cos I

A: 4. Given, y"+y=tanx

Q: dy h,p For problems 1-3 compute dx for the given set of parametric equations. and dx? 1. x = 7t2 –…

A: 1) Given that x=7t2-9t, y=t6+2t2We have to find the dydxand d2ydx2First we find…

Q: 4 cv16-x Use polar coordinate to evaluate Vx² + y² dy dx . Leave your answer correct to two decimal…

A:

Q: y" + 4y = 4 sin(2x)+ 8 cos(2x), y(0) = 0, y' (0) = 1.

A:

Q: y" + 4y" +y' – 6y = 2e¬t + 5 cos t y" + 4y' = 16 sin 2t , y(0) = 2, y'(0) = -2, y"(0) = 4

A:

Q: 2-(3%3-6%y)dx-(322+2y)dyso 3-(2%y%+siny)dx+(43y²+žcosy)dyso,

A: we given some differential equation . As per our guidelines I can only solve first question or first…

Q: T c •sinx, S* San* (1 + cosx)dydx 0, 0.

A: Given: The integration ∫0π∫0sinx1+cosxdydx To determine: The value of given integral.

Q: 4. Find the slope of the curve r = cos 20 at the origin 5. A particle moves along a path whose…

A:

Q: TY 7. Compute dy dx by converting to polar coordinates. V4-2 x2 + y2

A: 7. Given integral is ∫02∫-4-x20xyx2+y2dydx The objective is to solve the integral using polar…

Q: FIND Y(s) OF THE GIVEN EQUATION. y" + 4y = cos(t-3)+4t, y" - 6y + 15y = 2 sin(3t), y(3)=0_y' (3)=7 y…

A:

Q: FIND Y(S) OF THE GIVEN EQUATION. y" + 4y = cos(t-3) +4t, y(3)=0 y' (3)=7

A:

Q: 1 x =e" cos v, y=e" sinv uaz เมื่อ แ=1 และ "=- 3 และ ĉu Find

A:

Q: •5 25-x2 Evaluate (x² + y? )° dy dx by converting to polar coordinates.

A: To evaluate the integral using polar coordinates

Q: 2- y" + 4y' + 20 y = 23 sin t - 15 cos t y(0) = 0 , y'(0) = -1 %3D

A: Differential equation is, y''+4y'+20y=23sint-15cost Given conditions is, y0=-1y'(0)=1

Q: For problems 4 – 7 find the equation of the tangent line(s) to the given set of parametric equations…

A:

Q: п 4. Find the slope of the tangent line to the polar curve r = 1 – sin40 at 0 = 4 : a. 3 b. 4 c. 2…

A:

Q: 4. Solve for the critical points of the given parametric equation: x = t³ – 1; y = t² + t

A:

Q: i- y' + 2y 4 cos 2x. yT) = 3 (using Bernoulli Equation) %3D %3D

A:

Q: (1 + cos 2y) dr - 2r dy = 0, y(1) = i %3D Oy = Arctan 2 O y = Arctan O y = Arctan ( 1) D y = Arctan…

A:

Q: 8. Solve for the critical points of the parametric equations x = t3 – 1,y = t² +t %3D

A: The answer is found in step-2.

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x? +² =…

A: Here finds the parametric equation for the tangent line to the curve of intersection.   where the…

Q: 3. Solve the DE: 1 + 2.ry? ) dx + (2ya² – cos y) dy = 0, y(1) = || - -

A:

Q: 2y dy = sin dx when y(1) 4 + %3D -

A:

Q: 25) y" + y = 2 cos(t), y(0) = 2, y'(0) = 0.

A: Use second order differential equation

Q: Solve for the critical points of parametric equation x=t^3-1, y=t^2+t

A:

Q: d's 元 =-4 sin 2t-- 2 s'(0) = 100,s(0) = 0 %3D dt?

A:

Q: 8. Solve for the critical points of the parametric equations x = t - 1,y = t² +t

A: To find the critical points of parametric curve x(t)=t2-1, y(t)=t2+t

Q: 2. Given the parametric equations x= 2t+ sin 2t and y=1-cos 21, where t is a parameter, dx 2)

A:

Q: Obtain a solution to this linear equation. dx − (1 + 2x tan y) dy = 0

A: Given that: dx − (1 + 2x tan y) dy = 0

Q: The velocity of a particle moving in the xy plane is given by the parametric equations dx/dt=…

A: The given parametric equations of the particle is dxdt=-2t sin2t and dydt=2t cos2t. Evaluate the…

Q: Given that r= cos 0 ; dx = - sin 20 and de dy = cos 20. do The slope of the tangent line to the…

A:

Q: 19. y" + 2y + 5y = t cos 2t, y(0) = 1, y'(0) = 0

A:

Q: 3. y" + 2y' + 5y = t cos(5t) - 6,y(0) = 1, y'(0) = -2

A: