3.9.23 Problems 2201 to 2300

Table 3.551: First order ode linear in derivative

#

ODE

Mathematica

Maple

4528

y+xy=x2+y2

4529

(3x+2y+1)y+4x+3y+2=0

4530

(x2y2)y=2xy

4531

y+(1+y2e2x)y=0

4532

x2y+y2+x3y=0

4533

y2exy2+4x3+(2xyexy23y2)y=0

4534

y=(x2+2y1)23x

4535

xy+y=x2(1+ex)y2

4536

2yxyln(x)2xln(x)y=0

4537

y+ay=kebx

4538

y=(x+y)2

4539

y+8y3x3+2xy=0

4540

(xyx2y2+x)y=yx2x2y2

4541

y+ay=bsin(kx)

4542

xyy2+1=0

4543

(y2+asin(x))y=cos(x)

4544

xy=xeyx+x+y

4545

y+cos(x)y=esin(x)

4546

xyy(ln(xy)1)=0

4547

x3yy2x2y=0

4548

xy+ay+bxn=0

4549

xyyxsin(yx)=0

4550

y23xy2x2+(xyx2)y=0

4551

(6xy+x2+3)y+3y2+2xy+2x=0

4552

x2y+y2+xy+x2=0

4553

(x21)y+2xycos(x)=0

4554

(1+x2y)y+xy21=0

4555

(x21)y+xy3xy2=0

4556

(x21)y2xyln(y)=0

4557

(1+x2+y2)y+2xy+x2+3=0

4558

cos(x)y+y+(sin(x)+1)cos(x)=0

4559

y2+12x2y+(2xy+4x3)y=0

4560

(x2y)y+x=0

4561

(x2y)y4xy=0

4562

xyy+x2+y2=0

4563

2xyy+3x2y2=0

4564

(2xy3x4)y+2x3yy4=0

4565

(xy1)2xy+(1+y2x2)y=0

4566

(x2+y2)y+2x(y+2x)=0

4567

3y2yx+y32x=0

4568

2y3y+xy2x3=0

4569

(2xy3+xy+x2)yxy+y2=0

4570

(2y3+y)y2x3x=0

4571

yexy+ex=0

4675

ay3bx32+y=0

4676

axy3+by2+y=0

4677

yxay3+3y2xayx2a+ax1a=0

4678

y(yf(x))(yg(x))(yaf(x)+bg(x)a+b)h(x)f(x)(yg(x))f(x)g(x)g(x)(yf(x))g(x)f(x)=0

4679

x2y+xy3+ay2=0

4680

(ax+b)2y+(ax+b)y3+cy2=0

4681

y+ytan(x)=0

4685

y=eax+ay

4687

x(1y)y+(1+x)y=0

4688

y=axy2

4689

y2+xy2+(x2x2y)y=0

4690

xy(x2+1)y=1+y2

4691

xy+1=yy1+x

4692

y+b2y2=a2

4693

y=1+y2x2+1

4694

sin(x)cos(y)=cos(x)sin(y)y

4695

axy+2y=xyy

4731

y+y2=a2x4

4748

y=y

4749

xy=y

4750

x1y2+yx2+1y=0

4751

ysin(x)=yln(y)

4752

1+y2+xyy=0

4753

xyyxy=y

4754

y=2xy2+xx2yy

4755

yy+xy28x=0

4756

y+2xy2=0

4757

(y+1)y=y

4758

yxy=x

4759

2y=3(y2)13

4760

(x+xy)y+y=0

4761

y+y=ex

4762

x2y+3xy=1

4763

y+2xyxex2=0

4764

2xy+y=2x52

4765

cos(x)y+y=cos(x)2

4766

y+yx2+1=1x+x2+1

4767

(1+ex)y+2exy=(1+ex)ex

4768

xln(x)y+y=ln(x)

4769

(x2+1)y=xy+2xx2+1

4770

y+ytanh(x)=2ex

4771

y+cos(x)y=sin(2x)

4772

x=cos(y)xtan(y)

4773

x+xey=0

4774

x=3y23x3y

4775

y+y=xy23

4776

y+yx=2x32y

4777

3y2yx+3y3=1

4778

2xe3y+ex+(3x2e3yy2)y=0

4779

(xy)y+y+x+1=0

4780

cos(x)cos(y)+sin(x)2(sin(x)sin(y)+cos(y)2)y=0

4781

x2y+y2xy=0

4782

yy=x+x2+y2

4783

xy+(x2+y2)y=0

4784

y2xy+(xy+x2)y=0

4785

y=cos(x+y)