yp-x2q2-x2y=0
1. Differentiate of the following functions with respect to x:
i) 𝑆𝑖𝑛𝑥∙ ln(5𝑥)
ii) √𝑐𝑜𝑠√𝑥
iii) 𝑒 ln (𝑡𝑎𝑛5𝑥)
iv) 𝑆𝑖𝑛2 {ln(𝑠𝑒𝑐𝑥)}
v) ln (𝑡𝑎𝑛𝑥) �
write the ordinary differential equation (1+sin y)dx = (2ycosy-x(secy-tan y))dy
A 2000 L tank initially contains 40 kg of salt dissolved in 1000 L of water. A brine solution containing 0.02 kg/L of salt flows into the tank at a rate of 50 L/min. The solution is kept thoroughly mixed, and the mixture flows out at a rate of 25 L/min. (a) Find the quantity of salt in the tank at any time t > 0) prior to overflow. (b) Find the time of overflow.
solve the differential equation to the indicated inintial conditions; "y+4y=0" "y(0)=4" "y(0)=6"
Solve the following initial value problem
Ut(x,t)=10Uxx(x,t) -10
U(-1,t)=U(1,t) Ux(-1,t)=Ux(1,t) t>0
Ux(x,0)=x+1 -1
"{2xy cos\u2061\u3016x^2 \u3017-2xy+1}dx+{sin\u2061\u3016x^2 \u3017-x^2+3}dy=0"
Let f(x) = (x^2−1)/(x^4+1)
(a) At which points does the graph of the f(x) have a horizontal tangent line?
(b) Draw the graph of f(x) on MATLAB(or octave online) and identify the points for horizontal tangents on the graph.
Determine the general solution to the equation ∂2u/∂t2=c2(∂2u/∂x2) under the boundary conditions u(0,t)=u(1,t)=0 and initial conditions u(x,0)=Φ(x), ut(x,o)=Ψ(x)