Advertisements
Advertisements
Question
Solve the differential equation `dy/dx = (x + y+2)/(2(x+y)-1)`
Solution
`dy/dx = ((x+y)+2)/(2(x+y)-1)`
Let `x+y=t`
`1+ dy/dx =dt/dx rArr dy/dx = dt/dx-1`
`dt/dx-1= (t+2)/(2t-1)`
`dt/dx =(t+2)/(2t-1)+1`
`(dt)/dx = (t+2+2t-1)/(2t-1)`
`dt/dx=(3t+1)/(2t-1)`
`((2t-1)/(3t+1))dt = dx`
`2/3 int (6t -3)/(6t+2)dt=int dx`
`2/3 int((6t+2)-5)/((6t+2)) dt = x+C_1`
`2/3 int dt - 10/3 int dt/(6t + 2)=x+C_1`
`2/3t - 5/3 xx(In|3t+ 1|)/3 = x + C`
`2/3t - 5/9 xx(In|3t+ 1|) = x + C`
`2/3(x+y)-5/9In|3(x+y)+1|=x+C`
`2/3(x+y)- 5/9 In|3x +3y +1|=x+C`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int(x1+x^2)/(1+x^4)dx`
Evaluate: `int_-6^3 |x+3|dx`
If A, B and C are the elements of Boolean algebra, simplify the expression (A’ + B’) (A + C’) + B’ (B + C). Draw the simplified circuit.
Prove that locus of z is circle and find its centre and radius if is purely imaginary.
For the set A = {1, 2, 3}, define a relation R in the set A as follows: R = {(1, 1), (2, 2), (3, 3), (1, 3)}. Write the ordered pairs to be added to R to make it the smallest equivalence relation.
Let f: R → R be the function defined by f(x) = `1/(2 - cosx)` ∀ x ∈ R.Then, find the range of f
If R is a relation from a non – empty set A to a non – empty set B, then ____________.
Let A = {a, b, c}, then the range of the relation R = {(a, b), (a, c), (b, c)} defined on A is ____________.
Number of relations that can be defined on the set A = {a, b, c, d} is ____________.
Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}, then ______.
