Higher Engineering Mathematics, Sixth Edition
442 Higher Engineering Mathematics (c) the mid-ordinate rule, (d) Simpson’s rule. Give answers correct to 3 decimal places. 6. ∫ ...
Revision Test 13 This Revision Test covers the material contained in Chapters 43 to 45.The marks for each question are shown in ...
Chapter 46 Solution of first order differential equations by separation of variables 46.1 Family of curves Integrating both side ...
Solution of first order differential equations by separation of variables 445 x 10 20 30 y y 2 x 2 15 y 2 x 2 8 y 2 x ...
446 Higher Engineering Mathematics Integrating both sides gives: y= ∫ ( 2 x − 4 x^2 ) dx i.e. y=2lnx− 4 3 x^3 +c, which is the g ...
Solution of first order differential equations by separation of variables 447 5. 1 ex + 2 =x− 3 dy dx ,giveny=1whenx=0. [ y= 1 6 ...
448 Higher Engineering Mathematics Problem 8. (a) The variation of resistance, Rohms, of an aluminium conductor with temperature ...
Solution of first order differential equations by separation of variables 449 The rate of cooling of a body is given by dθ dt ...
450 Higher Engineering Mathematics Whenx=0,y=1 thus^12 ln1=ln1+c, from which, c=0. Hence the particular solution is^12 ln( 1 +x^ ...
Solution of first order differential equations by separation of variables 451 whereCpandCvare constants. Givenn= Cp Cv , show th ...
Chapter 47 Homogeneous first order differential equations 47.1 Introduction Certain first order differential equations are not o ...
Homogeneous first order differential equations 453 (iv) Separating the variables gives: x dv dx =v− 1 −v=− 1 , i.e.dv=− 1 x dx I ...
454 Higher Engineering Mathematics 47.4 Further worked problems on homogeneous first order differential equations Problem 3. Sol ...
Homogeneous first order differential equations 455 (v) Replacing v by y x gives: ln ( y^2 x^2 − 1 ) =lnx+c, which is the general ...
Chapter 48 Linear first order differential equations 48.1 Introduction An equation of the form dy dx +Py=Q,wherePand Qare functi ...
Linear first order differential equations 457 48.2 Procedure to solve differential equations of the form dy dx +Py=Q (i) Rearran ...
458 Higher Engineering Mathematics (iv) Substituting in equation (3) gives: yex= ∫ ex(x)dx (4) (v) ∫ ex(x)dx is determined using ...
Linear first order differential equations 459 Let 3 x− 3 (x+ 1 )(x− 2 ) ≡ A (x+ 1 ) + B (x− 2 ) ≡ A(x− 2 )+B(x+ 1 ) (x+ 1 )(x− 2 ...
460 Higher Engineering Mathematics In an alternating current circuit containing resistance R and inductanceLthe current i is gi ...
Chapter 49 Numerical methods for first order differential equations 49.1 Introduction Not all first order differential equations ...
«
19
20
21
22
23
24
25
26
27
28
»
Free download pdf