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Differential Equations
4. a) A wet porus substance in the open air loses its moisture at a rate proportional to the moisture
content. If a sheet hung in the wind loses half its moisture during the first hour, then find the
time when it has lost 95% moisture provided the weather conditions remain the same.
b) If the interest is compounded continuously, the amount of money invested increases at a rate
proportional to its size. Let Rs. 10,000 be invested at 10% compounded continuously. Then in
how many years will the original investment double itself ?
c) Solve: dy/dx + (x/1-x^2) y = xy, y(0)=1.
content. If a sheet hung in the wind loses half its moisture during the first hour, then find the
time when it has lost 95% moisture provided the weather conditions remain the same.
b) If the interest is compounded continuously, the amount of money invested increases at a rate
proportional to its size. Let Rs. 10,000 be invested at 10% compounded continuously. Then in
how many years will the original investment double itself ?
c) Solve: dy/dx + (x/1-x^2) y = xy, y(0)=1.
Differential Equations
3. d) A mass m (in kgs) acted on by a constant force p Newtons, moves a distance x in t sec.
and acquires a velocity v m/ s . Show that
x = mv^2 / 2gp = gt^2p / 2m
where g is the acceleration due to gravity.
and acquires a velocity v m/ s . Show that
x = mv^2 / 2gp = gt^2p / 2m
where g is the acceleration due to gravity.
Differential Equations
3. a) Write a suitable form of particular solution for solving the equation
y'' + 3y' + 2y = e^x (x^2 + 1) sin 2x + 3e^-x cos x + 4e^x
by the method of undetermined coefficients.
b) Verify that e^x and xe^x are solutions of the homogeneous equation corresponding to the
equation
y''− 2y'+ y = e^x / (1 + x^2), −&<x<&
and find the general solution using the method of variation of parameters.
c) If y1 = 2x+2 and y2 = -x^2 / 2 are the solutions of
xy' + y' - y'^2 / 2
then are the constant multiples c1 y1 and c2 y2 , where c1 and c2 are arbitrary, also solutions
of the given differential equation? Is the sum y1 + y2 a solution? Justify your answer.
y'' + 3y' + 2y = e^x (x^2 + 1) sin 2x + 3e^-x cos x + 4e^x
by the method of undetermined coefficients.
b) Verify that e^x and xe^x are solutions of the homogeneous equation corresponding to the
equation
y''− 2y'+ y = e^x / (1 + x^2), −&<x<&
and find the general solution using the method of variation of parameters.
c) If y1 = 2x+2 and y2 = -x^2 / 2 are the solutions of
xy' + y' - y'^2 / 2
then are the constant multiples c1 y1 and c2 y2 , where c1 and c2 are arbitrary, also solutions
of the given differential equation? Is the sum y1 + y2 a solution? Justify your answer.
Differential Equations
y=2x^3-9x^2+12x+5 it has minima at x=2 and maxima at x=1. my question is any other maxima or minima can be found except those point?
Differential Equations
y=x+(1/x). can we find any other maxima or minima at any other point except x=1 and -1.i sketch the graph , at x=1 there is a minima and x=-1 there is a maxima . but can not understand from graph why the maxima is less than the minima.
Differential Equations
what can be the graph of a curve where there is no maxima and minima?
Differential Equations
Solve the following ODE using the power series method: (1 - X^2) y" - 2xy' + 2 y = 0
Differential Equations
Solve the initial value problem: d^2x /dt^2 + 2 dy/dx - 3x = 0, X(2pie) = 1, x^.(2pie) = 13
Differential Equations
Solve the following ordinary differential equations: I) ( 2y + X^2 + 1) dy /dx + 2 xy - 9x^2 = 0? 2) d^2y /dx^2 + 3*dy/dx + 2y = X^2
Differential Equations
Obtain all the first and second order partial derivatives of the function: f ( x, y ) =ln ( 1 + xy ^ 2)
