Knowing that y (0) = 1 and y' (0)= 1, find a specific solution for: d²y +3-10y 0 dx? dx y = ÷e*. - 5x y = 7 5x y=2e*+5e+ y = 2 e7* +5 e

Q: fx) D, f(쪽) -1, and f(플) %=D1, and COSX 3 f) = -1. Find S f(x) dx. %3D

A: Given that  f'x=cosxx, fπ2=-1 and f3π2=1find ∫π23π2fxdx

Q: Find y': 5a? – 2x?y? + 4y3 – 7 = 0. |

A: Explanation: Given that,  5x2-2x2y2+4y3-7=0

Q: Solve the equation dy, 3y + dx +2 = 3x, y(1) = 1.

A:

Q: dy ху Solve dx (1+y2)

A:

Q: dy 1 csc(x) -csc(x) y = y* dx

A:

Q: X-5 If y = Inx , find y'(e²).

A: If the two functions f(x)and g(x)are differentiable (i.e. the derivative exist) then the quotient is…

Q: Substitute the expressions from the previous steps. Then substitute (x, y) = (1, 1) and solve for dy…

A: To find the slope of the tangent line to the curve  at the point .

Q: dy Find for each equation and simplify fully. dx (17x² + B) (11x – A)° (а). у- (5x+4)°

A: Given                             y=17x2+B511x-A85x+46; A=4, B=8 we have to find derivative of the…

Q: Let xy = 2y + x. If you implicitly differentiate this dy equation, and then solve for you dx (a-y)…

A:

Q: n/3 sec23x 8. n/4 2+4tan 3x dx

A:

Q: dfy = 12 - 30x, y'(0) = 7, and y(0) = 2. dx2 Find the function y(x) satisfying = 12 - 30x, y'(0) =…

A: Given:

Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: What is exact solution for dy/dx =(x2+y2)/(x+y)

A: Given: The given equation is dydx=(x2+y2)x+y

Q: T/2 V1+cosx dx T/3

A:

Q: d²y + 4y = 8x² ,y(0) = -3,y'(0) = 0 dx2

A: We have to solve the differential equation using initial conditions.

Q: Find y'. O A. 2x+ O B. 2x- ОС. 2х+ -| -| |

A: we have y=x+1xx-1x

Q: x? + 4x + 1 dx (x - 1)(x + 1)(x + 3)

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: If the characteristic poynomial ofa matrix A is der 21 -A)= -32°+32°+2 then det(2.4) =

A:

Q: dy Y=2x² In x dx X

A:

Q: 4 xf (x* )dxif f(x)dx = 5. Find Enter the exact answer. f (x* )dx=

A: given:-∫04f(x)dx=5now∫-20xf(x2)dxlet,x2=t2xdx=dtxdx=12dtx=-2,    t=4x=0 ,       t=0

Q: If y=x^(2)+81, find the relationship between (dy)/(dt) and (dx)/(dt) Where x,y depend upon t.

A: We have to find the relationship between  and where  and  depend upon .We use Chain Rule to answer…

Q: (2xe + e*)dx + (x² + 1)e'dy = 0

A:

Q: Abbie has 3 hours left to film. She lights a new Candle Type A and Candle Type B and then starts…

A: Let after x hours candle A and candle B has same height. First Let represent the height of candleh,…

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.