A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 mg of materials present, and after 2 hours, it is observed that the material has lost 10% of its original mass. Find the mass of the material after 4 hours. 45 mg O 40.50 mg O 42.50 mg 43.75 mg

Q: DIFFERENTIAL EQUATION: Find the general solution using separation of variables with step by step…

A: Solution

Q: 1 dr 3

A:

Q: dy dx || (2y + 3 4x + 5/ 2

A:

Q: 2. Solve the differential equation: a. y' = xe-sinx – y cos x

A: We will solve the problem

Q: Calculate t* cos(4t), where * denotes convolution. t* cos(4t) =

A:

Q: Sin () dy %3D XCSC

A: Given sinyxdydx-1=yx cscyx, y(1)=0 Dividing both sides by  sinyx dydx-1sinyx=yx cscyx1sinyx…

Q: 2++ (* +*) v - 0 ey (cv + ) • v/ = 0

A:

Q: Obtain the particular solution when x = 1 and y = 1 3 y°) dx 3 - x(x + y) dy = 0

A:

Q: x³ y" + x² y" = 1

A: Here, the differential equation is given by x3y'''+x2y''=1. The general solution of the differential…

Q: ) 24?y'txy2-x³=0

A:

Q: y' − 2 ² = y² X 2. -

A: First order linear differential equations:

Q: usine Solve the differential Equation by of andetermined cofficients coeffic CD² +6D + 8) Y = x +…

A:

Q: 6. -4s 2 S

A:

Q: Question 1: Write any two non-zero elements from the given subsets. (a). S₁ {(a, b, c)| a+b=2+c} ≤…

A:

Q: Differential Equation with coefficient linear in two variables   (x+2y-1)dx+(3x+6y-5)dy=0

A: Given a differential equation with coefficient linear in two variable (x+2y-1) dx + (3x+6y –…

Q: Prove that Ho Ge) =(-1) e" ď e dx 2. 2.

A:

Q: n to grow at a rate proportional to the amount present. After 60 minutes, 5,000 strands of the…

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: dy dx = xy + 3x - y - 3 xy - 2x + 4y - 8

A:

Q: y = Ce- 2 + C2e3

A: Given equation is y=C1e−2x+C2e3x......1. We have to eliminate the arbitrary constants. Differentiate…

Q: ot tre eqiatan (X-xy+y?)g'=xy Find the Solutun Rtcon which passes thirongh the point (2,1).

A: The equation is, (x2xy+y2)y'=xy               dydx=xy(x2xy+y2) Take y=vxdiff with respect to x,…

Q: dy/dx% 3 sec 2xsec3y

A:

Q: Differential equation Demonstrate the following relationship. e^x = sinhx+coshx

A: Use the following formulae, to obtain the solution.…

Q: 10. Find the equation of a line with a slope of -3, passing through (2,-5). y=mx+b m= (x, y) = ( D

A:

Q: Differential Equation Show a comple te solution 11 2X 2-y-ay e t2

A: Firstly, we find complementary function by solving auxillary equation

Q: Solve en

A:

Q: dy -sec y dx = 0 sec x %3D

A: We will find out the required general solution.