3.9.2 Problems 101 to 200

Table 3.509: First order ode linear in derivative

#

ODE

Mathematica

Maple

101

6y+xy=3xy43

102

y3e2x+2xy=2xy

103

x4+1y2(xy+y)=x

104

y3+3y2y=ex

105

3y2yx=3x4+y3

106

eyxy=2ey+2e2xx3

107

2xcos(y)sin(y)y=4x2+sin(y)2

108

(ey+x)y=1+xey

109

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

110

4xy+(x+6y)y=0

111

3x2+2y2+(4xy+6y2)y=0

112

3x2+2xy2+(2x2y+4y3)y=0

113

x3+yx+(ln(x)+y2)y=0

114

1+exyy+(exyx+2y)y=0

115

cos(x)+ln(y)+(ey+xy)y=0

116

x+arctan(y)+(x+y)y1+y2=0

117

3x2y3+y4+(3x3y2+4xy3+y4)y=0

118

exsin(y)+tan(y)+(excos(y)+xsec(y)2)y=0

119

2xy3y2x4+(x2y2+1y+2yx3)y=0

120

2x523y532x52y23+(2x52+3y53)y3x32y53=0

121

x3+3yxy=0

122

3y2+xy2x2y=0

123

xy+y2x2y=0

124

ex+2xy3+(sin(y)+3y2x2)y=0

125

3y+x4y=2xy

126

2xy2+x2y=y2

127

2x2y+x3y=1

128

2xy+x2y=y2

129

2y+xy=6x2y

130

y=1+x2+y2+y2x2

131

x2y=xy+3y2

132

6xy3+2y4+(9y2x2+8xy3)y=0

133

y=1+x2+y2+x2y4

134

x3y=x2yy3

135

3y+y=3x2e3x

136

y=x22xy+y2

137

ex+exyy+(ey+exyx)y=0

138

2x2yx3y=y3

139

3x5y2+x3y=2y2

140

3y+xy=3x32

141

(1+x)y+(x21)y=1

142

xy=12x4y23+6y

143

ey+cos(x)y+(eyx+sin(x))y=0

144

9y2x2+x32y=y2

145

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

146

9xy4312x15y32+(8x32y1315x65y)y=0

147

3y+x3y4+3xy=0

148

xy+y=2e2x

149

y+(2x+1)y=(2x+1)32

150

y=3x2(7+y)

151

y=3x2(7+y)

152

y=xy+xy3

153

y=3x22y24xy

154

y=3y+x3x+y

155

y=2x+2xyx2+1

156

y=cot(x)(yy)

415

y=1+y2

448

3y+y=e2t+t

449

2y+y=e2tt2

450

y+y=1+tet

451

yt+y=3cos(2t)

452

2y+y=3et

453

2y+ty=sin(t)

454

2ty+y=2tet2

455

4ty+(t2+1)y=1(t2+1)2

456

y+2y=3t

457

y+ty=t2et

458

y+y=5sin(2t)

459

y+2y=3t2

460

y+y=2e2tt

461

2y+y=te2t

462

2y+ty=t2t+1

463

2yt+y=cos(t)t2

464

2y+y=e2t

465

2y+ty=sin(t)

466

4t2y+t3y=et

467

(t+1)y+ty=t

468

y2+y=2cos(t)

469

y+2y=et3

470

2y+3y=eπt2

471

(t+1)y+ty=2tet

472

2y+ty=sin(t)t

473

cos(t)y+sin(t)y=et

474

y2+y=2cos(t)

475

2y3+y=t2+1

476

y4+y=3+2cos(2t)

477

y+y=1+3sin(t)

478

3y2+y=2et+3t

479

y=x2y

480

y=x2(x3+1)y

481

sin(x)y2+y=0

482

y=3x213+2y

483

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

484

xy=1y2

485

y=ex+xey+x

486

y=x21+y2

487

y=(2x+1)y2

488

y=2x+1y

489

x+yyex=0

490

r=r2x